Assisted zero voltage switching for a DCtoDC converter
An apparatus includes a first auxiliary switch connected to a positive connection of a switching leg of a DCtoDC converter. The switching leg includes a first main switch and a second main switch connected at a main switch midpoint. A second auxiliary switch is connected between a negative connection of the switching leg and the first auxiliary switch. A connection point between the first and second auxiliary switches is an auxiliary midpoint. An auxiliary inductor connects the auxiliary midpoint and the main switch midpoint. The main switch midpoint is also connected to other converter elements. The first and second main switches include a first capacitance a second capacitance. A switch regulation module regulates the first and second auxiliary switches to control current in the auxiliary inductor to provide or remove charge from the first and second capacitances to induce zero voltage switching for the first and second main switches.
Latest UTAH STATE UNIVERSITY Patents:
 MINIATURIZED GREEN ENDBURNING HYBRID PROPULSION SYSTEM FOR CUBESATS
 BATTERYBASED SYSTEM FOR POWERING REFRIGERATED TRANSPORT AND OTHER INDUSTRIAL APPLICATIONS
 Materials for use in an aqueous organic redox flow battery
 Echo cancelation using convolutive blind source separation
 Constant DC current input to constant DC voltage output power supply covering a wide programmable range
This application claims the benefit of U.S. Provisional Patent Application No. 62/006,734 entitled “DIRECT CURRENT TO DIRECT CURRENT CONVERTER” and filed on Jun. 2, 2014 for Regan Zane, et al., which is incorporated herein by reference. “Modeling and Control of the Dual Active Bridge Series Resonant Converter,” Ph.D. dissertation of Daniel Seltzer, submitted to the Faculty of the Graduate School of the University of Colorado, Department of Computer, and Energy Engineering, Jul. 18, 2014 is hereinafter incorporated by reference.
FIELDThis invention relates to direct current (“DC”) to DC converters and more particularly relates to assisted zero voltage switching for DCtoDC converters.
BACKGROUNDAs electrical systems increasingly come to dominate modern life, the power conversion technologies that enable these systems to efficiently connect to one another are becoming increasingly important. With the expanding demand for such technologies in ever diversifying areas, the demands placed on power converters have increased in kind. For many years switching converters have been able to keep up with these increasing requirements by adopting ever more complex power converter topologies and control schemes. One major development in this area is the class of resonant switching converters, such as the series resonant converter. These types of converters have allowed higher efficiency power conversion with faster response times in a variety of applications. Their cost lies in the greater difficulty with which they are modeled (and thus controlled), and is frequently substantial.
SUMMARYAn apparatus for assisted zero voltage switching is disclosed. A system and method also perform the functions of the apparatus. The apparatus includes a first auxiliary switch connected to a positive connection of a switching leg of a direct current (“DC”) to DC converter. The switching leg includes a first main switch and a second main switch, where the first and second main switches are connected at a main switch midpoint. The apparatus includes a second auxiliary switch connected between a negative connection of the switching leg and the first auxiliary switch, where a connection point between the first and second auxiliary switches is an auxiliary midpoint. The apparatus includes an auxiliary inductor connected between the auxiliary midpoint and the main switch midpoint. The main switch midpoint is also connected to elements of the converter in addition to the first and second main switches and the auxiliary inductor. The first and second main power switches turn on and off as part of operation of the converter. The first main switch includes a first capacitance and the second main switch includes a second capacitance. The apparatus also includes a switch regulation module that regulates switching of the first and second auxiliary switches to control current in the auxiliary inductor. The auxiliary inductor provides or removes charge from the first capacitance and the second capacitance to adjust voltage across the first main switch and the second main switch to induce zero voltage switching for the first and second main switches.
In one embodiment, the first capacitance may be capacitance of the first main switch and/or a capacitor connected in parallel with the first main switch, and the second capacitance may be capacitance of the second main switch and/or a capacitor connected in parallel with the second main switch. In another embodiment, the apparatus includes a current sensing module that senses current in the auxiliary inductor and in the connection between the elements of the converter and the main switch midpoint. The switch regulation module uses current sensed by the current sensing module and switching states of the first and second main switches to regulate switching in the first and second auxiliary switches to adjust current in the auxiliary inductor to adjust voltage across the first and second main switches to achieve zero voltage switching.
In one embodiment, the switch regulation module controls current in the auxiliary inductor by controlling a phase angle between a voltage transition at the auxiliary midpoint and the main switch midpoint. In another embodiment, the switch regulation module controls the phase angle according to the equation:
where

 Φ_{N }is the phase angle between the voltage transition at the auxiliary midpoint and the main switch midpoint;
 f_{s }is the switching frequency of the converter;
 L_{aux }is inductance of the auxiliary inductor;
 t_{d }is a dead time between switching of the first main switch and the second main switch;
 C_{N }is capacitance of one of the first capacitance and the second capacitance;
 V_{A }is voltage of the power source;
 i_{x }(t) is current in the connection between the elements of the converter and the main switch midpoint; and
 λ is +1 when the first main switch is on and −1 when the second main switch is on.
In one embodiment, the converter is a resonant power converter. In another embodiment, the resonant power converter includes at least one stage of a dual active bridge series resonant converter (“DABSRC”). In another embodiment, the first and second main switches include a first switching leg of a full bridge switching network of the converter, where the converter includes a third main switch connected to the positive connection of a second switching leg and a fourth main switch connected to negative connection of the second switching leg. The first and second switching legs form a full bridge switching network, which includes a third auxiliary switch connected to the positive connection of the second switching leg, a fourth auxiliary switch connected to a negative connection of the second switching leg, and a second auxiliary inductor connected to a second auxiliary midpoint between the third and fourth auxiliary switches and a second main switch midpoint between the third and fourth main switches. The third main switch includes a third capacitance and the fourth main switch includes a fourth capacitance.
In the embodiment, the switch regulation module regulates switching of the third and fourth auxiliary switches to control current in the second auxiliary inductor. The second auxiliary inductor provides or removes charge from the third capacitance and the fourth capacitance to adjust voltage across the third main switch and the fourth main switch to induce zero voltage switching for the third and fourth main switches. In a further embodiment, the converter is a DABSRC converter, where the full bridge switching network is a first full bridge switching network on a primary side of the converter and the converter also includes a second full bridge switching network on a secondary side of the converter and each switching leg of the second full bridge switching network includes two auxiliary switches and an auxiliary inductor controlled by a switch regulation module to achieve zero voltage switching of switches in the second full bridge switching network.
In one embodiment, the switch regulation module operates independent of feedback control loops of the converter. In another embodiment, the apparatus includes a ZVS activation module that activates switching of the first and second auxiliary switches and the switch regulation module when the converter is in a hard switching condition. In another embodiment, the converter includes a DABSRC converter with a current feedback loop, where the current feedback loop includes compensation implemented using a gain scheduled feedback controller. The gain scheduled feedback controller includes one or more output control signals that vary over a plurality of control regions, where the gain scheduled feedback controller implements a different compensation equation for each control region.
In a further embodiment, the converter includes one or more phase shift modulators controlled by the one or more output control signals, where the one or more output control signals control according to a minimum current trajectory (“MCT”) control technique. The MCT substantially minimizes circulating current within the converter. In another further embodiment, the gain scheduled feedback controller maintains at least a portion of the main switches of the converter in a ZVS region while minimizing circulating current by following a trajectory a fixed distance from an MCT for a portion of operating regions of the converter and the switching regulation module controls auxiliary switches connected to at least a portion of the main switches of the converter to maintain zero voltage switching when the main switches connected to the auxiliary switches operate in a hard switching operating region.
A system for assisted ZVS includes a DCtoDC converter with one or more switching legs. Each switching leg includes two main switches connected at a main switch midpoint where a first main switch of the switching leg is connected between a positive connection of the switching leg and the main switch midpoint and a second main switch of the switching leg is connected between the main switch midpoint and a negative connection of the switching leg. Each switching leg includes a portion of a half bridge switching network or a full bridge switching network. The system includes an assisted ZVS apparatus connected to one or more switching legs of the converter. Each ZVS apparatus of a switching leg includes a first auxiliary switch connected between an auxiliary midpoint of the switching leg and the positive connection of the switching leg, a second auxiliary switch connected between the auxiliary midpoint and the negative connection of the switching leg, and an auxiliary inductor connected between the auxiliary midpoint and the main switch midpoint of the switching leg. The main switch midpoint connects to elements of the converter in addition to the first and second main switches of the switching leg. The first and second main power switches turn on and off as part of operation of the converter, and the first main switch includes a first capacitance and the second main switch includes a second capacitance. Each switching leg with auxiliary switches and an auxiliary inductor also includes a switch regulation module that regulates switching of the first and second auxiliary switches to control current in the auxiliary inductor, where the auxiliary inductor provides or removes charge from the first capacitance and the second capacitance to adjust voltage across the first main switch of the switching leg and the second main switch of the switching leg to induce zero voltage switching for the first and second main switches. In one embodiment, the system includes an electronic device powered by the converter.
A method for zero voltage switching includes regulating switching of a first auxiliary switch and a second auxiliary switch to control current in an auxiliary inductor. The auxiliary inductor provides or removes charge from a first capacitance of a first main switch of a switching leg and a second capacitance of a second main switch of the switching leg to adjust voltage across the first main switch and the second main switch to induce zero voltage switching for the first and second main switches. The switching leg includes a portion of a DCtoDC converter. The first and second main power switches turn on and off as part of operation of the converter. The first auxiliary switch is connected to a positive connection of the switching leg and to an auxiliary midpoint, the second auxiliary switch is connected between the auxiliary midpoint and a negative connection of the switching leg, and the auxiliary inductor is connected between the auxiliary midpoint and a main switch midpoint, the main switch midpoint is a connection between the first main switch and the second main switch, and the main switch midpoint connected to elements of the converter in addition to the first and second main switches and the auxiliary inductor.
In one embodiment, the method includes sensing current in the auxiliary inductor and in the connection between the elements of the converter and the main switch midpoint and regulating switching of the first and second auxiliary switches includes using the current sensed in the auxiliary inductor and in the connection between the elements of the converter and the main switch midpoint and using switching states of the first and second main switches to regulate switching in the first and second auxiliary switches to adjust current in the auxiliary inductor to adjust voltage across the first and second main switches to achieve zero voltage switching. In another embodiment, regulating switching of the first and second auxiliary switches includes controlling current in the auxiliary inductor by controlling a phase angle between a voltage transition at the auxiliary midpoint and the main switch midpoint. In another embodiment the switching leg is a first switching leg of the converter and the converter includes additional switching legs and the method includes regulating switching of first and second auxiliary switches to control current in an auxiliary inductor associated with each additional switching leg to achieve zero voltage switching in the main switches of each additional switching leg.
In order that the advantages of the invention will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings, in which:
with Φ_{DC}=180°, and Φ_{AD}=90°;
with Φ_{AB}=180°, and Φ_{DC}=180°;
with Φ_{AB}=180°, Φ_{AD}=90°;
Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment, but mean “one or more but not all embodiments” unless expressly specified otherwise. The terms “including,” “comprising,” “having,” and variations thereof mean “including but not limited to” unless expressly specified otherwise. An enumerated listing of items does not imply that any or all of the items are mutually exclusive and/or mutually inclusive, unless expressly specified otherwise. The terms “a,” “an,” and “the” also refer to “one or more” unless expressly specified otherwise.
Furthermore, the described features, advantages, and characteristics of the embodiments may be combined in any suitable manner. One skilled in the relevant art will recognize that the embodiments may be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments.
These features and advantages of the embodiments will become more fully apparent from the following description and appended claims, or may be learned by the practice of embodiments as set forth hereinafter. As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method, and/or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, microcode, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module,” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having program code embodied thereon.
Many of the functional units described in this specification have been labeled as modules, in order to more particularly emphasize their implementation independence. For example, a module may be implemented as a hardware circuit comprising custom VLSI circuits or gate arrays, offtheshelf semiconductors such as logic chips, transistors, or other discrete components. A module may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices or the like.
Modules may also be implemented in software for execution by various types of processors. An identified module of program code may, for instance, comprise one or more physical or logical blocks of computer instructions which may, for instance, be organized as an object, procedure, or function. Nevertheless, the executables of an identified module need not be physically located together, but may comprise disparate instructions stored in different locations which, when joined logically together, comprise the module and achieve the stated purpose for the module.
Indeed, a module of program code may be a single instruction, or many instructions, and may even be distributed over several different code segments, among different programs, and across several memory devices. Similarly, operational data may be identified and illustrated herein within modules, and may be embodied in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network. Where a module or portions of a module are implemented in software, the program code may be stored and/or propagated on in one or more computer readable medium(s).
The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention.
The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A nonexhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (“RAM”), a readonly memory (“ROM”), an erasable programmable readonly memory (“EPROM” or Flash memory), a static random access memory (“SRAM”), a portable compact disc readonly memory (“CDROM”), a digital versatile disk (“DVD”), a memory stick, a floppy disk, a mechanically encoded device such as punchcards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiberoptic cable), or electrical signals transmitted through a wire.
Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instructionsetarchitecture (“ISA”) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, statesetting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on a computer, partly on the computer, as a standalone software package, partly on the computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, fieldprogrammable gate arrays (“FPGA”), or programmable logic arrays (“PLA”) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention.
Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions.
These computer readable program instructions may be implemented in hardware, may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks.
The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks.
Although various arrow types and line types may be employed in the flowchart and/or block diagrams, they are understood not to limit the scope of the corresponding embodiments. Indeed, some arrows or other connectors may be used to indicate only the logical flow of the depicted embodiment. For instance, an arrow may indicate a waiting or monitoring period of unspecified duration between enumerated steps of the depicted embodiment. It will also be noted that each block of the block diagrams and/or flowchart diagrams, and combinations of blocks in the block diagrams and/or flowchart diagrams, can be implemented by special purpose hardwarebased systems that perform the specified functions or acts, or combinations of special purpose hardware and program code.
I. Definitions and NotationFull signal quantities are defined as the sum of both large signal (generally constant) portions of a signal as well as the time varying small signal portion. Lower case letters with capital subscripts are used to represent these full signal quantities,
i_{T}=I_{T}+ĩ_{t}, (1)
where the large signal component is represented using a capital letter and a capital subscript. The small signal portion of a signal is represented using both lowercase letters and subscripts with the addition of a tilde. Time domain signals use parenthesis, as in ν_{IN}(t) for the time varying signal ‘ν_{IN}’, while frequency domain signals are represented by their Fourier series coefficients using square brackets and an overhat. Using this notation the signal ν_{IN}(t) would be represented by its Fourier series coefficients as {circumflex over (ν)}_{IN}[n] in the frequency domain. Phasor signals are represented with an overbar, such that phasor
s_{x}(t,ω_{s})=Re[
The frequency that a phasor exists in is determined either by the context of the specific derivation or by an explicit statement. Phasors at zero frequency are assumed to exist and are equivalent to constant quantities such that the DC voltage ν_{IN}=
Complex quantifies use the variable ‘j’ to represent the complex variable. Double bars are used to represent the magnitude of complex quantities, with an angle symbol representing phase. Additionally the use of a super script represents the complex conjugate of a number, while a “*” used between elements designates convolution. Super scripts are used to designate the parameter with which a quantity has been derived in respect to. Finally, angled brackets are used for normalized values with a possible subscript to designate the normalizing quantity. Digitized signals may be represented as underlined symbols, e.g. the digitized output voltage V_{OUT }is V_{OUT}, which may be used interchangeably with V_{OUT}.
II. Converter Topologies and the DABSRCDue to the many demonstrated advantages of a dual active bridge series resonant converter (“DABSRC”), a DABSRC topology is selected for this work. This typically topology provides high efficiency and good power density for the 1 kW, 500 V target operating range. Additionally, the DABSRC is a wellknown converter which provides input/output isolation and bidirectional power flow. Other topologies may also be used with regard the embodiments of the proposed invention described herein.
II.1 Overall System
In one embodiment, the resonant power converter 100 is a DABSRC, as will be shown hereafter. Alternatively, the resonant power converter 100 may be a half bridge resonant converter as will be shown hereafter. In other embodiments, the resonant power converter 100 may include other resonant converter topologies. The resonant power converter 100 receives gate drive signals 110 from the modulator 290 and in response to the gate drive signals 110 converts an input DC voltage to an output DC voltage as will be described hereafter. The resonant power converter 100 may have a sensed output voltage V_{OUT}, a sensed input voltage V_{IN}, a sensed output current I_{OUT}, and a sensed input current I_{IN}. One or more sensors may measure the sensed output voltage V_{OUT}, the sensed input voltage V_{IN}, the sensed output current I_{OUT}, and the sensed input current T_{IN}. The sensed output voltage V_{OUT}, the sensed input voltage V_{IN}, the sensed output current I_{OUT}, and the sensed input current I_{IN }may be digital or analog signals.
In one embodiment, the digital signal conditioning module 205 receives the sensed output voltage V_{OUT}, sensed input voltage V_{IN}, sensed output current I_{OUT}, and sensed input current I_{IN }and generates digital representations converter output voltage V_{OUT}, an converter input voltage V_{IN}, an converter output current I_{OUT}, and an converter input current I_{IN }as will be described hereafter. In one embodiment, the converter output voltage V_{OUT}, the converter input voltage V_{IN}, the converter output current I_{OUT}, and the converter input current Ī_{IN }are equivalent to the sensed output voltage V_{OUT}, the sensed input voltage V_{IN}, the sensed output current I_{OUT}, and the sensed input current T_{IN }respectively. The converter output voltage V_{OUT}, the converter input voltage V_{IN}, the converter output current I_{OUT}, and the converter input current I_{IN }may be digital signals.
The main power flow controller 215 may receive the converter output voltage V_{OUT}, the converter input voltage V_{IN}, the converter output current I_{OUT}, and the converter input current I_{IN}. In addition, the main power flow controller 215 may receive reference signals such as a power reference P_{SET}, a voltage reference V_{SET}, and a current reference I_{SET}. The master controller 295 may generate the power reference P_{SET}, voltage reference V_{SET}, and current reference I_{SET}.
The main power flow controller 215 may generate control signals 280 that drive a plurality of phase shift modulators 230 of the modulator 290 to generate the gate drive signals 110 that operate the resonant power converter 100. The main power flow controller 215 may operate the resonant power converter 100 with a resonant tank current equal to a dynamic target resonant current. The dynamic target resonant current may be selected to minimize the resonant tank current. In one embodiment, the dynamic target resonant current is selected to minimize the resonant tank current while achieving a desired resonant converter output power. In a certain embodiment, the dynamic target resonant current is selected to satisfy (3):
In one embodiment, each phase shift modulator 230 of the modulator 290 generates 50% duty cycle square wave pulses that control the semiconductor switches 105. The functions of the elements of the DC to DC converter 10 are described hereafter.
II.2 DABSRC Description
The resonant power converter 100 includes a plurality of semiconductor switches 105 and a resonant tank 155. Each semiconductor switch 105 is activated and deactivated in response to a gate drive signal 110.
In the depicted embodiment, the resonant tank 155 includes an inductor L_{R}, a capacitor C_{R}, and a transformer 120. The gate drive signals 110 activate and deactivate first switches 111 to generate an alternating voltage and a resonant tank current 257 across the resonant tank 155. The gate drive signals 110 further activate and deactivate second switches 112 to rectify the alternating voltage and generate a desired DC voltage at the output 143.
In the depicted embodiments, the resonant tank 155 includes an inductor L_{R }and a capacitor C_{R}. The gate drive signals 110 activate and deactivate first switches 111 to generate an alternating voltage and a resonant tank current 257 across the resonant tank 155. The gate drive signals 110 further activate and deactivate second switches 112 to rectify the alternating voltage and generate a desired DC voltage at the output 143.
In order to achieve a high bandwidth output current control, a new model for the DABSRC is derived based on the phasor analysis and equivalent transformer work previously developed. This new model is used to derive control to output transfer functions for the DABSRC, and exposes the high degree of variability in control to output gain based on converter operating point experienced in the topology. Because the converter being designed must operate over a wide range of both power levels and conversion rations, a gain scheduled approach may be used for feedback regulation of output current.
A fixed frequency phase shift modulated switching method is selected for the DABSRC. By adopting the MCT approach, RMS tank currents I_{T }are kept to a minimum, thus increasing overall converter efficiency. Although a number of other switching methods are possible, the MCT approach lends itself well to variable conversion ratio application.
In order to achieve soft switching of the DABSRC over the wide range of operating conditions required by this application, a PSM auxiliary leg approach is taken. This method is used without the DC blocking capacitors typically employed, based on work showing that in certain cases inductively linked half bridges do not require the DC blocking capacitors.
The outlier detection/removal module 610 may filter out spurious signals, noise, and other outlier values from the sensed output voltage V_{OUT}, sensed input voltage V_{IN}, sensed output current I_{OUT}, and sensed input current I_{IN}. The data averaging module 615 may calculate a moving average for each of the sensed output voltage V_{OUT}, sensed input voltage V_{IN}, sensed output current I_{OUT}, and sensed input current T_{IN}. The offset removal module 620 may remove value offsets and/or signal bias from each of the sensed output voltage V_{OUT}, sensed input voltage V_{IN}, sensed output current I_{OUT}, and sensed input current I_{IN }to generate the converter output voltage V_{OUT}, converter input voltage V_{IN}, converter output current I_{OUT}, and converter input current I_{IN}.
III Modeling the DABSRCIn order to achieve a high bandwidth output current regulation, a new model for the DABSRC is developed. The model sought relates each of the three possible control angles for the DABSRC independently to both the input and output currents of the converter. The derivation begins with an analysis of the active bridge switch network. This analysis leads to the equivalent transformer as a way to linearize the effects of the switch network. This linearization enables the use of common circuit analysis techniques in order to derive the desired control to output relations for the DABSRC.
III.1 the Equivalent Transformer in Steady State
The equivalent transformer allows active switch networks in power converters to be replaced with a “transformer” model with a time varying conversion ratio. When the equivalent transformer is constrained to a single frequency it is the same as the phasor transformer, and performs the function of converting DC waveforms into phasor waveforms. This process is equivalent to using fundamental analysis to solve a circuit although graphically it tends to be more intuitive. The derivation of the full equivalent transformer model begins with harmonic analysis of a general half bridge switch network. This analysis leads to the full equivalent transformer model, which is then simplified to the phasor transformer.
where (5) represents the complex valued Fourier Series coefficients of (4) and angular switching frequency ω_{s}=2π/T_{s}. Using (5) to represent the switch node voltage of a single halfbridge in the frequency domain the output voltage of a fullbridge switch network can be defined as the difference of two such series,
with phase angles φ_{A }and φ_{AB }allowing phase shift modulated control of the full bridge network as seen in
Series (7) relates the input and output voltage of the full bridge switch network in the same way as a transformer turnsratio relates input and output voltages of an ideal transformer. For this reason it is defined as the “equivalent turnsratio” of the full bridge switch network. As the reciprocal of (7) is not well defined in this form, the equivalent transformer only allows voltages to be computed from input to output, and current to be computed from output to input when stated in this way.
The output current of the full bridge switch network can be described as its own series
î_{2}[n]=k_{2}[n]e^{jφ}^{2}^{[n]} (8)
where phase shift φ_{2 }and gain k_{2 }are dependent on the impedance seen by the full bridge output and thus unknown. In a conventional transformer the output current (8) would be multiplied by turns ratio (7) in order to determine the input current. By using a discrete convolution in place of simple multiplication this is still the case in the frequency domain for the equivalent transformer,
Applying the definition of convolution seen in (9) to the full bridge voltage relation as well, a symmetrical set of equations can be used to describe a full bridge switch networks voltage and current conversion ratios,
î_{1}[n]=ŝ_{N}[n]*î_{2}[n], (10)
Equations (10) and (11) represent the voltage and current conversions performed by a full bridge switch network in a form similar to that of a traditional transformer, and allow such networks to be replaced with equivalent transformer models in the frequency domain.
To ease calculations the infinite series in (10) and (11) are commonly replaced with finite approximations. This can be done by selecting an integer N such that
where the truncation error ε has a computable upper bound and can be made arbitrarily small with larger values of N. As the magnitude of higher harmonics drops off sharply, (12) is an acceptable approximation for even small values of N. These two factors allow truncation error ε to be ignored for most practical choices of N, resulting in a finite series representation for f(t) in the frequency domain using only a small number of Fourier series coefficients.
To ensure that harmonics above N are not reintroduced to the system through multiplication, a truncated form of discrete convolution is introduced,
This truncation is similar to assuming that a system does not exist above frequencies indexed by N, which is a common simplification when modeling converters. By substituting truncated series for all voltages and currents in (10) and (11) and using (13) for convolution, a finite series approximation of the equivalent transformer is defined.
In many systems approximating complex waveforms with their fundamental harmonic is accurate enough to allow meaningful results without overly complicated computation. This is easily achieved with the equivalent transformer model by setting N=1 in (12) and (13). Selecting this value for N allows many simplifications and results in the “phasor transformer” model of a full bridge switch network. This form of the equivalent transformer has previously been used to analyze time varying circuits and is derived here for use in resonant converters as a subset of the equivalent transformer. Although some of the final equations reached in this section have previously been seen, their relation to the full frequency content of converter signals has been neglected until now.
Because current i_{2 }and turns ratio s_{N }both have zero average value and represent realvalued waveforms, (10) can be simplified into
Due to the relationship between a real signal's fundamental frequency phasor representation and its Fourier coefficients,
where
In (16),
Equation (11) can also be simplified under the assumption that s_{N }and ν_{2 }both have zero average value. Beginning with the definition of the truncated Fourier series for ν_{2 }from (13) with N=1,
For systems in which the input voltage is assumed constant, the phasor
Using these equations and the equivalent circuit for the phasor transformer as a model for switch networks greatly simplifies the analysis of the DABSRC. Equations (20) and (19) are all that is needed for steady state analysis, while small signal models follow by extension and are discusses below.
III.2 Steady State Analysis
Steady state analysis of the DABSRC focuses on enabling three tasks. First, it must be possible to design a converter whose output meets basic design specifications. Once this is accomplished maintaining reasonable component stresses becomes the focus. Finally, once a converter with acceptable output capabilities and reasonable component stresses has been designed the steady state control space must be investigated in order to achieve the highest steady state efficiency. In actuality these three areas are closely coupled with each other such that none may be individually optimized. As is generally the case in such situations, an iterative design methodology is applied. The rigorous three parameter constrained optimization problem possible in this situation is left to future work.
Although the design process for the DABSRC is of necessity iterative, logically the steps involved are well organized. First the tank currents and voltages are calculated, leading to expressions for RMS voltage and currents as well as component stress approximations. These expressions are then used to calculate power flow at both input and output for three angle control of the DABSRC. Finally the resonant tank values and switching components are selected based on the previous analysis.
for primary and secondary switch networks, respectively. Equations (21) and (22) result from application of (15) onto (7) with N=1. For the remainder of this paper, n is assumed to equal one in order to simplify examples and derivations.
Assuming a constant input and output voltage, the applied tank voltages
Applying these voltages across the complex tank impedance with the inclusion of series resistor R_{r }to model tank losses
evaluated at the switching frequency ω_{s }defines the steady state phasor tank current,
Conversion ratio M is defined as output voltage ν_{OUT }over input voltage ν_{IN }times the transformer turns ratio n.
Using (26), the RMS tank current can be found as
with the theoretical maximum RMS tank current
when φ_{AB}=φ_{AD}=φ_{DC}=π.
The peak resonant capacitor voltage can be found as the scaled magnitude of the time integral of ī_{T}. The actual value of this maximum voltage depends on whether a split capacitor is used or not, but is easily derived in either case. For a single capacitor on the secondary side of the tank isolation transformer, this voltage is found to be equal to
When a primary side resonant capacitor is used, the resulting in a maximum capacitor voltage is found to be n times (29). For a split capacitor system such as the one shown in
Equations (28) and (29) relate to the maximum theoretical values across all possible control angles. When control angles are constrained to follow a set path in the three dimensional control space, these actual maximum values encountered may be far smaller.
Input and output currents for the DABSRC are found by applying (19) directly to the converter model in
Multiplying by the appropriate voltage results in expressions for the input and output powers with respect to the three control angles used. Doing so results in a simple expression for the maximum possible output power assuming an ideal tank,
achieved at φ_{AB}=φ_{DC}=π and φ_{AD}=π/2. Determining the maximum output power with a nonzero tank resistance is best done with a numerical optimization, as the resulting shift in tank current phase results in slightly modified control angles needed to achieve the maximum available power output.
Equations (26)(32) along with the associated phase and magnitude for phasor quantities fully define all steady state signals of the DABSRC according to a fundamental approximation. These results allow a power stage to be intelligently designed according to project specifications.
Based on steady state analysis of the DABSRC, a V_{IN}=500 V converter is designed with a nominal conversion ratio of M=1. A switching frequency of f_{s}=100 kHz is chosen. Because the ratio of RMS tank current to delivered output current is lowest at a unity conversion ratio, a transformer turns ratio of n=1 is chosen. A nominal output power of P_{o}^{MAX}=1 kW is desired, helping to force the selection of tank parameters using (32). This output power must be maintained down to a conversion ratio of M=0.4, while at M=1 a pulsed power of P_{o}^{BURST}=2 kW must be delivered. These constraints allow (32) to be solved for the magnitude of the tank impedance necessary at the switching frequency,
An additional constraint on the tank impedance is set by requiring the maximum resonant capacitor voltages to remain below 400 V for the split tank capacitor design seen in
A combination of these constraints can now be used to determine the specific tank parameters, resulting in a resonant tank inductance of L_{r}=200 μH and a total resonant capacitance of C_{r}=34 nF. C_{r }is implemented as a split capacitor using two capacitors of twice the nominal value located on either side of the isolation transformer. This is done in order to ensure that zero average current is maintained in both the primary and secondary windings of the tank transformer without the need for average current control. This simple approach for maintain zero average current has the drawback of increasing the tank volume. In order to remove this issue, it may be possible to use a single capacitor due to the inherent voltsecond balancing achieved in some resonant converters, although this extension is left for future revisions. L_{r}, is additionally split in order to increase symmetry for the input bridges.
III.3 Small Signal Analysis of the DABSRC
Small signal analysis of the DABSRC begins with defining a small signal model of the phasor transformer. This derivation is done assuming that an ideal voltage source is used as an input on the primary side with an arbitrary impedance loading the secondary side of the transformer model. Perturbations are applied to control angles only with the input voltages of each equivalent transformer assumed to be constant. The primary side equivalent transformer input voltage is defined as the constant DABSRC input voltage, while the secondary side equivalent transformer input voltage is defined as the constant DABSRC output voltage. By perturbing each of the control angles, small signal voltage perturbations on the applied AC tank voltage is predicted. Once a small signal model for the phasor transformer has been derived, it is inserted into a linearized small signal model of the full DABSRC with small signal phasor tank impedance. This converter model is used to derive small signal tank currents, and used in conjunction with the large signal model of the converter derived in Section III.2 above in order to derive small signal input and output currents.
Beginning with the nonzero terms of (6), the first two terms of a two variable Taylor series expansion around a steady state phase vector V_{Φ}={Φ_{A},Φ_{AB}} can be used as a linear approximation of the equivalent transformer output voltage,
Equations (36) and (37) represent the linear approximation of the effect of φ_{A }and φ_{AB }perturbations on ν_{2 }and can be represented as two complex voltage sources in series on the secondary side of the equivalent transformer.
Due to the small signal voltage sources from (35), current i_{2 }will react dependent on the relation between ν_{2 }and i_{2 }in circuit. Regardless of the specific relation, current i_{2 }will react with magnitude and phase perturbations,
î_{2}[n]=(K_{2}[n]+{tilde over (k)}_{2 }[n])e^{j(φ}^{2}^{[n]+{circumflex over (φ)}}^{2}^{[n])} (38)
Applying the transformer relation from (10) to (38) results in a nonlinear input current in terms of the magnitude and phase of i_{2}, as well as the phase control angles φ_{A }and φ_{AB}. Using a four variable Taylor series expansion this expression can be linearized as a sum of small signal sources,
The difficulty in directly applying (39) results from the need to expand the small signal tank magnitude and phase in terms of the two control angle variables. Because this expansion includes terms dependent on the unknown ν_{2}−i_{2 }relation, (39) is left as is for the general form of the equivalent transformer small signal model. An example of expanding (39) once the tank impedance is known is given later in this section for the DABSRC.
Phasor representation of inductors and capacitors as small signal elements has been previously dealt with. The results, duplicated here for clarity, show that capacitors and inductors require the addition of an imaginary resistance,
where R_{C }is added in parallel with C_{r }and R_{L }added in series with L_{r }as seen in
This expression is equivalent to evaluating (25) at (ω_{s}−js). Resistors, current sources, and voltage sources retain their form, with voltage and current source values converted into their phasor equivalents. To complete the small signal model of the DABSRC, only the small signal representation of the phasor transformer need be applied.
Rephrasing (36) and (37) in terms of the converter control angles and applying (15) in order to achieve phasor quantities results in three small signal phasor sources. The single control angle applied to the primary switch network results in a single small signal source resulting from a sum of (36) and (37) evaluated with n=+1,
The secondary side switch network results in a pair of small signal sources, after collecting terms for each of the two control angles,
The small signal tank current is computed as a function of the three small signal voltage sources (43)(45) applied across the tank impedance (42) and can be split into real and imaginary portions,
To obtain magnitude and phase envelopes for the tank current of the DABSRC, the complex phasor relation in (46) is split into two real functions which separately relate magnitude and phase to each of the three control angle perturbations. This has previously been done for the magnitude envelope of a phasor signal, but not for the phase envelope of a phasor signal. Both equations are derived by linearizing the equations for the magnitude and phase of a complex number in rectangular form with a first order Taylor series expansion. For some phasor g with steady state complex value G=G_{X}+jG_{Y }and small signal value g={tilde over (g)}_{x}+j{tilde over (g)}_{y }this results in
Applying (47) and (48) to (46) results in expressions for the linearized effect of each of the three control angles on both the magnitude and the phase of the small signal tank current phasor,
The order of the transfer functions in (49)(50) depends directly on the small signal tank impedance. Due to the form of (47) and (48), the three transfer functions in (49) have equal order to the number of zeroes in the small signal tank impedance, while the three transfer functions in (50) have a highest possible order of the number of zeroes in the small signal tank impedance squared.
To derive linear models for the input and output currents relation to each of the three control angles requires revisiting a large signal model of the DABSRC. Linearizing the large signal input and output currents in (30) and (31) results in expressions for small signal perturbation in terms of the tank current components found in (49) and (50). This is done by treating the tank current and phase as quantities with no dependence on control angle, and then using the chain rule to expand the result in terms of the dependence on each of the three control angles. After substituting the correct quantities, the desired results are achieved.
Beginning with the large signal input current of the DABSRC derived previously,
partial derivatives are taken with respect to both the tank current magnitude K_{T }and tank current phase φ_{T}, as well as with respect to the three control angles,
For the input current, two of these terms are zero as there is no direct dependence on either φ_{AD }or φ_{DC}. The dependence of k_{T }and φ_{T }on the three control angles is dealt with by using the chain rule to expand the first two terms of (52),
Each of the six partial derivatives in (53) and (54) with respect to the three control angles have been previously derived in (49) for the tank current magnitude and in (50) for the tank current phase. Substituting the results into (53) and (54) and canceling terms results in expressions for the partial derivative of the input current with respect to both tank current and tank phase perturbations which are dependent on only the three control angles perturbations,
Inserting (55) and (56) into (52) results in the desired equation for the small signal input current. These equations can now be rearranged into three separate terms, each relating a single control angle with small signal input current perturbations,
In (58)(60), each of the partial derivatives is a gain term dependent on steady state operating point, while each of the multiplying terms is a transfer function as found previously.
Solving for the small signal output current follows the same process, beginning with the large signal output current,
Taking partial derivatives with respect to each of the three control angles as well as the tank current magnitude and phase results in a sum of six quantities just as before,
with the only difference being that the output current has a direct dependence on both φ_{AD }and φ_{DC}, with no direct dependence on φ_{AB}. The derivation proceeds from (62) just as it did for the input current, resulting in three terms which each relate a single control angle to small signal output current,
The desired results for both input and output current small signal models are found in (57) and (63). The transfer functions seen in these equations have orders dependent on the tank current transfer functions in (49) and (50). Each of these equations provides a linear relation between control action from any of three control inputs and either input or output current. The constants used in each of these equations are summarized in Table 1.
With the derivation of small signal models relating each of the three control angles to both input and output currents of the DABSRC completed, a feedback controller for the converter can be implemented.
Control of the DABSRC begins with determining the optimal set of control angles for steady state operation in terms of converter efficiency. This optimization can include both RMS tank currents as well as ZVS regions for the converter; although the future inclusion of PSMHB auxiliary circuitry on all bridges means that an optimization on only RMS tank currents is performed. Once this is completed, the small signal models developed for the DABSRC are used to determine a feedback controller using the control angle trajectories determined decided upon.
Due to the way in which the ZVS circuitry is designed control of the PSMHB auxiliary legs is dealt with completely separately from control of the main power stage as shown below with respect to PSM leg ZVS assistance control. This allows a greatly simplified derivation for a high bandwidth ZVS control loop.
Finally, once controllers for the DABSRC and its associated ZVS circuitry are derived, the input and output regulated converter is augmented with both voltage and power control loops. These output control loops allow for simplified series and parallel connection between converters, and are the last step in designing a controller for the DABSRC.
IV.1 Operation Along the MCT
For a lossless resonant tank, the steady state output power of the DABSRC assuming P_{OUT}^{MAX }as seen in (30)
is a function of all three control angles, while the maximum output power is a function of the converter tank design, operating frequency, and input and output voltages. Normalizing by the maximum output power the expression for the normalized output power of the converter,
is equal to the expression for the normalized output current of the converter assuming an ideal voltage source on the output of the DABSRC,
Due to this equivalency, a normalized output command variable,
U_{OUT}=I_{OUT}=P_{OUT} (70)
is defined. With this notation, each desired normalized output U_{OUT }has an associated actual output U_{OUT }which exists between the maximum achievable normalized output+U_{OUT,MAX}=1 and the minimum achievable normalized output, −U_{OUT,MAX}=−1.
The RMS tank current of the DABSRC is also defined as a function of the three converter control angles, as seen previously in (27). As the RMS tank current is directly related to conduction losses, the optimal selection of steady state converter control angles is one which minimizes the RMS tank current while still achieving the desired normalized output command.
For a given steady state output command the goal is to operate the converter with the minimum RMS tank current possible. This objective is equivalently expresses by the following constrained minimization problem,
whose solutions are the minimum current points of U_{OUT}; as U_{OUT }varies in the possible range of outputs, the solution describes a trajectory in the control space ν_{φ}, referred to as the minimum current trajectory (MCT). Using the results from above regarding tank voltage and currents and steady state power flow with three angle modulation, (71) can be stated as a system of trigonometric equations, the solution of which can be put in closed form. The form of these solutions depends on the conversion ratio M as follows:
When M≦1: The MCT is a 2D curve lying on the φ_{DC}=π plane. For U_{OUT}≧(1−M^{2})^{1/2 }the MCT consists of a single branch in which φ_{AB}=π while φ_{AD }controls converter output power/current. This branch along which only φ_{AD }varies is denoted as γ_{2}. For U_{OUT}≦(1−M^{2})^{1/2 }the MCT splits into two branches, γ_{1+} and γ_{1−}, on which power/current flow is controlled by both φ_{AD }and φ_{AB}. Analytical expressions for the MCT in the M<1 case are
When M≧1: The MCT is a 2D curve lying on the φ_{AB}=π plane. For U_{OUT}≧(1−M^{2})^{1/2 }the MCT consists of a single branch in which φ_{DC}=π while φ_{AD }controls converter output power/current. This branch along which only φ_{AD }varies is denoted as k_{2 }and is equivalent to γ_{2}. For U_{OUT}≦(1−M^{2})^{1/2 }the MCT splits into two branches, λ_{1+} and λ_{1→} on which power/current flow is controlled by both φ_{AD }and φ_{DC }Analytical expressions for the MCT in the M>1 case are
For either of the above cases when trajectories λ_{1±} and γ_{1±} are used the bridge with the higher voltage operates with a phase shift not equal to π, while the bridge with the lower voltage operates with a phase shift equal to π. This scheme results in a minimum voltage difference across the tank, as the high voltage bridge is modulated to reduce the applied voltagesecond waveform. Due to the reduced difference in applied voltages across the tank the peak values of the tank current waveform are reduced, thus reducing the RMS value of the waveform. Both cases collapse to the same solution at a conversion ratio of M=1. At this conversion ratio single angle modulation of φ_{AD }alone along either γ_{2 }or equivalently λ_{2 }is shown to minimize RMS tank currents.
It is useful to construct the tank phasor diagram as the operating point moves along the MCT from P_{OUT}=0 up to P_{OUT}=P_{OUT}^{MAX}. In what follows, the phasor associated with voltage ν_{X}(t) is denoted with V_{X}.
Let us discuss case M<1 first. For U_{OUT}<(1−M^{2})^{1/2}, two operating points Q_{γ+}(P_{OUT}) and Q_{γ−}(P_{OUT}) exist, as illustrated in
The phasor arrangement illustrated in
Reverse power operation (P_{OUT}<0) results in similar phasor diagrams, with the current phasor 180° phaseshifted with respect to
Case M>1 can be discussed using similar arguments but with the roles of the two bridges exchanged. Along λ_{1}, minimum current operation for M>1 can be equivalently defined as the condition in which the input bridge delivers the maximum voltage (φ_{AB}=180°) while angles φ_{DC }and φ_{AD }are modulated so as to maintain unity input power factor (I in phase with V_{AB}). As predicted by (75), this condition can be maintained up to U_{OUT}=(1−M^{−2})^{1/2}. Beyond such point, the minimum current trajectory proceeds along λ_{2}.
Case M=1 can be regarded, at this point, as a boundary situation in which no phasor arrangement exists to force the tank current I to be in phase with V_{AB }or V_{DC}′. This explains why only γ_{2}like solutions exist in this case, as described by either (74) or (75).
The foregoing phasor analysis provides an explanation for the existence of different branches in the minimum current trajectories and of an intermediate power level above which the minimum current solution changes its analytical structure.
In this Section the switching behavior of the electronic devices when the DABSRC is operated along the minimum current trajectory is discussed. Only case M<1 is discussed in detail, as the symmetrical case M>1 can be treated similarly by exchanging the roles of the two bridges and by replacing M with 1/M in the analytical expressions.
Consider the phasor diagram illustrated in
U_{OUT}≦√{square root over (M·(1−M))} (76)
These results extend the analysis reported in [22], in which the zerovoltage switching boundary condition for the M<1 case was expressed as cos(φ_{AD})=M, here written according to the notation used in this paper. From (67) and with φ_{AB}=φ_{DC}=180°, the corresponding critical power level is found to be U_{OUT}=(1−M^{2})^{1/2}, which represents the breaking point between the γ_{1± }branches and the γ_{2 }branch in the minimum current trajectory as predicted by (9.a).
Nonetheless, comparison between the hard switching vs. soft switching boundaries along the oneangle modulation trajectory and along the proposed MCT shows, as illustrated in
IV.2 Gain Scheduling Feedback Control
Once steady state operating angles have been determined, a dynamic controller can be derived. Having previously generated small signal models relating control angle perturbations to input and output current perturbations, the small signal relation between the output command control variable and the minimum current trajectory control angles still must be derived. Once this has been completed, a small signal model of the DABSRC controlled along the minimum current trajectories may be assembled. Using this model, loop gains are analyzed and used to design a feedback controller for input and output current control. Due to the nature of the open loop system controlled in this way, a gain scheduled feedback controller is ultimately used.
In Section III.3 regarding small signal analysis of the DABSRC, transfer functions relating each of the three control angles to either the input or output current were derived. In order to control the DABSRC along the MCT, a small signal model must be derived relating the control input U_{OUT }to the control angle vector. Once this relation has been derived, a full small signal model of the DABSRC controlled along the MCT is complete.
From the trajectories in (74) and (75), only branches γ_{1+}, γ_{2}, and λ_{1+} will be used as they cover the whole control space. A similar derivation is possible if trajectories γ_{1→}, γ_{2}, and λ_{1− }are chosen. The results are symmetric if a 180° rotation around φ_{AB}=π, φ_{AD}=0 for M<1 and φ_{DC}=π, φ_{AD}=0 for M>1 is performed.
Taking the partial derivative of branches γ_{1+}, γ_{2}, and λ_{1+} with respect to the command variable U_{OUT},
results in nine gain terms. In (77)(79) the partial derivatives of each control angle with respect to the output command are taken assuming that the control angle is on the trajectory given, with the results summarized in Table 2 above.
Using (77)(79), piecewise linear gains are defined for each of the three control angles depending on converter operating point,
Using these three gains relating each control angle to the output command, a final set of transfer functions is assembled to relate output command variations directly to output current variations using equations (63)(66),
Equation (84) is the desired result, as it allows control of the DABSRC using an output command variable. Derivation of a transfer function useful for feedback control of the DABSRC using an input command variable follows the same steps as above, with all output quantities replaced by the equivalent input quantity.
Mathematically the gains seen in Table 2 present a problem at the point where the γ_{1+} and γ_{2 }trajectories touch for M<1 and at the point where the λ_{1+} and γ_{2 }trajectories touch for M>1. When these points are approached from lower magnitude output command towards higher magnitude power commands, the MCT begins to run parallel to contours of constant output command. At these points the small signal MCT gain reaches an infinite value, requiring an infinite change in control angle to achieve a change in output variable. The same phenomenon occurs at both the maximum and minimum output commands, for a similar reason. Although mathematically real and understandable, the effect is mitigated in a real system due to a number of nonidealities. The main consequence of this effect is that simulations must avoid these points in order to avoid nonfinite transfer functions.
All plots exhibit a large spike in gain at a frequency equal to the switching frequency of the converter minus the tank resonant frequency as expected. Although located at the same frequency for all operating points, the associated phase drop can be seen to vary across both conversion ratio as well as output command. In addition to slight phase differences between operating points, a large variation in gain is seen in all plots, with both the low frequency gain as well as the resonant spike gain varying across both conversion ratio and output command.
Due to the variability in both gain and phase of the control to output transfer function (84) demonstrated in
For applications which require a consistent response from the converter regardless of operating point, a gain schedule may be built which maintains a constant bandwidth regardless of operating points. With this approach, the worst case operating point is the operating point at which the lowest possible bandwidth is achieved while still maintaining phase margin P_{M}≧P_{M}_{_}_{MIN }and gain margin G_{−M}≧G_{M}_{_}_{MIN }for stability. At all other operating points, integral gains K_{i }are solved for which maintain the bandwidth found at the worst case point, BW_{SET}. Although providing consistent response characteristics, this type of gain schedule results in larger than needed gain and phase margins over much of the operating space and a lower bandwidth than necessary at most operating points.
In contrast to a gain schedule which maintains a constant bandwidth, a gain schedule may be derived which maintains a fixed phase or gain margin across all operating points. With this type of a gain schedule, the maximum possible bandwidth at all points can be achieved while maintaining constant stability margins. While providing higher bandwidths than the previous approach, this type of controller results in a less consistent response characteristic as operating point is varied. For either gain scheduling approach, a script may be used to calculate a gain table based on scheduling variables U_{CMD }and M. This two dimensional table is then referenced into using the converter operating point in order to select the proper gain.
Contrasting these two gain scheduled controllers is a fixed gain approach. In this case a single gain is solved to maintain stability at the worst case operating point. At this single worst case operating point, all three approaches provide the same response. As operating point is varied, a fixed gain controller results in excessive stability margins leading to low bandwidth responses, as well as an inconsistent response characteristic.
For the DABSRC design described above in Section III.2, a gain schedule is derived which provides the maximum possible bandwidth at all operating points. Stability is ensured by requiring a phase margin P_{M}≧55° and a gain margin G_{M}≧10 dB. The input voltage is again assumed to be V_{IN}=500 V, with conversion ratios between M=0.1 and M=1.2, corresponding to output voltages between V_{OUT}=50 V and V_{OUT}=600 V.
Although small signal stability is maintained at all points by the gain schedule designed above, a large signal analysis of stability with this approach has not been performed.
IV.3 MultiMode Control
In order to add the ability to regulate output voltage and output power to the current controlled DABSRC, multimode control is used. Not only does this extension provide the needed voltage and power regulation, but it also allows for the series and parallel connection of multiple converters into a single module with natural power sharing. This approach uses a limit curve for each of the three control variables (power, voltage and current) in order to achieve the desired results.
An apparatus 7900 for multimode control of a converter is presented. The apparatus may be implemented with the converter 10 depicted in
The multimode control apparatus 7900 may also include a positive power regulation module 7904 that controls output power P_{OUT }of the converter to the positive power reference P_{SET }over a positive constant power range between the output voltage of the converter being at the output voltage reference V_{SET }and output current I_{OUT }of the converter being at a positive output current reference I_{SET}, which may be described simply as the current reference I_{SET}. As depicted in
The multimode control apparatus 7900 may also include a negative power regulation module 7906 that controls output power P_{OUT }of the converter to the negative power reference −P_{SET }over a constant power range between output voltage V_{OUT }of the converter being at the output voltage reference V_{SET }and a maximum negative power limit of the converter. For example, the negative power reference −P_{SET }may be set lower than the maximum negative power limit of the converter. As depicted in
The multimode control apparatus 7900 may also include a constant current module 7908 that limits output current to a positive output current reference I_{SET }in a range between a minimum output voltage and output power P_{OUT }of the converter reaching the positive power reference P_{SET}. As depicted in
Note that an input, i.e. 141 and an output, i.e. 143 may be a matter of perspective. For example, the input 141 may be connected to a voltage source and/or a load and the output may be connected to a load that is capable of syncing and sourcing current so that in one mode the voltage source provides power to the load and in another mode the load provides power to a load connected to the input 141 of the converter 10. In this embodiment, the input and output may switch when the load provides power to the converter 10. In this condition, the input and output of the converter 10 may be reversed and
In one embodiment, the constant current module 7908 includes a current feedback control loop that limits output current I_{OUT }to below the positive output current reference I_{SET}. In another embodiment, the positive power regulation module 7904, the negative power regulation module 7906, and the voltage regulation module 7902 include feedback control loops and the current feedback control loop is an inner feedback control loop and the feedback control loops of the positive power regulation module 7904, the negative power regulation module 7906, and the voltage regulation module 7902 make up an outer feedback loop. The current feedback loop is discussed below. One implementation of the control loops is depicted in
In one embodiment, the constant current feedback loop includes compensation implemented using a gain scheduled feedback controller, as described above in Section IV.2 and may be configured as shown in
In one embodiment, the output voltage reference V_{SET }varies with output current I_{OUT }such that the output voltage reference V_{SET }decreases as output current I_{OUT }increases. In another embodiment, the positive output current reference I_{SET }varies with output voltage V_{OUT }such that the positive output current reference I_{SET}, which may also be referred to herein as the converter current reference, decreases as output voltage V_{OUT }increases. Operation of a module along a current limit curve may result in converter power sharing as long as all converters in a module are connected in parallel. Series operation of current limited converters may prove problematic in certain embodiments, as this leaves each individual converter with an uncontrolled output voltage. A simple approach with no communication between modules is to use droop control by adding a slope to the current limit line (
When a module made up of series connected converters is operated in current regulation mode, the output voltage of any two converters may be mismatched by as much as the full module voltage, such that a single converter processes the full module power. The addition of R_{1 }reduces this theoretical maximum converter voltage offset when operated in series, ∥ΔV_{S}∥, to
∥ΔV_{S}∥=R_{1}ΔI_{ε}, (86)
where ΔI_{ε} represents the maximum current sensing error between converters.
Operation along a voltage limit line achieves inherent power sharing in modules made up of series connected converters, while parallel connected converters in a voltage regulating module are left with an uncontrolled output current. This issue is solved with the introduction of a slope on the voltage limit line (
V_{set}(I_{O})=V_{Set}(0)−I_{OUT}R_{V} (87)
Without R_{V }parallel connected converters regulating voltage may have an output current offset equal to the full current processed by the module. R_{V }reduces this theoretical maximum converter current difference when operated in parallel, ∥ΔI_{P}∥, to
When operating on the power limit curve, automatic power balance of both parallel and series converters are achieved naturally. As all interconnected converters in a single module share a common voltage (parallel connection) or a common current (series connection), all converters in that module regulate to the same operating point when given equal power commands. For power limit control the maximum difference in converter power processing is simply equal to the converter power sensing accuracy.
In a practical application, the voltage mode slope R_{V }is a small value (ideally 0Ω), while the current mode slope R_{1 }is a large value (ideally infinite).
To simplify the extension of MMC to bidirectional converters it is assumed that symmetrical limit curves are used, such that the maximum forward current and power are the same as the maximum reverse current and power. The converter output voltage is assumed to remain positive.
While operating in current regulation mode, the appropriate converter current reference is simply I_{Set}(V_{OUT}),
I_{Ref}^{i}=I_{Set}(V_{OUT}) (89)
No additional compensator is needed, as the converter internal feedback loop already exists.
Using (87) and (89) for voltage and current reference points, controllers C_{V}(s) and C_{P}(s) in
The error signal for voltage regulation is the difference between the desired V_{Set }value and the measured output voltage, V_{OUT}. The addition of a voltage regulating compensator, C_{V}(s) results in a current reference for voltage regulation of
I_{Ref}^{ν}=C_{V}(V_{Set}−V_{OUT}). (90)
T_{V}(s)=C_{V}H_{iout}(Z_{O}+R_{V}). (91)
Feedback control of a current regulated converter along a power limit line is complicated by the nonlinear relation between output current and output power P_{OUT}. Although a number of methods exist for dealing with nonlinear feedback loops, one solution is to simply linearize the element. For the system in question the resulting linearized output current to output power gain K_{V }becomes dependent on the three set points such that it exists within a range
In general this is not ideal as the power regulation controller must be designed at the worst case point operating point. With this highly variable gain in the feedback loop, this will likely require an overly conservative controller design.
The loop gain for this setup takes the form
T_{P}(s)=C_{p}H_{iout}Z_{O}. (93)
Assuming that R_{V }is small in comparison with the worst case output impedance, both the voltage loop and the power loop gain are the same if the gainschedule method previously discussed is adopted for power control. In this case only one controller needs to be derived.
Only a voltage controller is derived as it was shown above that the same controller may be used for both voltage and power regulation assuming small R_{V}. This controller is then used for the power control loop as well without further modification.
The voltage regulator is designed to provide a bandwidth of 2 kHz under the worst case load using a second order controller. Assuming an output capacitance of this results in f_{z1}=728 Hz, f_{z2}=1.15 kHz, and A_{V}=0.025, with f_{P }set to a suitably high frequency of 10 f_{z1}. The controller is then converted into a digital form using a bilinear transform with frequency prewarping at the desired crossover frequency of 2 kHz. The resulting Zdomain controller takes the form
The controller in (94) is designed to achieve a bandwidth of approximately 10 times less than the current regulation internal loop. When used with the gain scheduled approach seen in Section VI.2 discussing a gain scheduled feedback controller this approach allows the external voltage and power loops to achieve high bandwidth as well.
V. Zero Voltage Switching Techniques for the DABSRCA large variety of auxiliary circuitry aimed at ensuring softswitching have been developed. These circuits can for the most part be grouped into two categories: passive (commonly using magnetizing inductance or shunt circuitry methods) and active (using active switching networks or advanced control schemes). Passive schemes have the benefit of little to no additional control complexity, while active auxiliary circuitry allows feedback and/or feed forward control of softswitching assistance. This additional control freedom can translate to lower losses and higher system efficiency at the cost of increased control complexity.
Five different ZVS methods warrant consideration for the DABSRC. These include modifying tank magnetics in order to increase magnetizing inductance, two different forms of auxiliary leg assistance, inductively linking converter modules, and modifying the MCT in order to extend the natural ZVS regions of the converter.
Modifying tank magnetics requires reducing the magnetizing inductance of the isolation transformer in
Auxiliary legs used for ZVS assistance may be controlled in one of two ways. The first involves PWM control of the inductively linked auxiliary halfbridge switches in order to store energy needed for ZVS transition of the main switches. A resonant transition then discharges the inductor current into the main switch node in order to achieve ZVS. By relying on the resonant transfer of energy, this approach requires the main switch node capacitance to be well known. Due to the nonlinear nature of many switching devices output capacitances, this approach is suited only for converters which utilize relatively large additional switch node capacitance in order to slow down switching transitions. Additionally, this approach does not allow ZVS of the auxiliary switches turn on transition, and so is poorly suited for high voltage applications.
Similar to PWM control of auxiliary legs, phase shift modulated (PSM) control may also be used. This approach generates a trapezoidal current in the auxiliary inductor of sufficient magnitude to force ZVS of the main switch node. While larger RMS currents are required in the auxiliary inductor for this approach, its lack of dependence on a resonant transition makes it easier to control. In addition, ZVS transitions for all switching elements are achieved. For these reasons it is a more attractive option for ZVS assistance of higher voltage DABSRCs which do not employ extra switch node capacitance.
If multiple converters are operated together as a module, either the primary or secondary legs of two such converters may be inductively linked. The analysis of this approach is the same as for PSM auxiliary legs, with the added condition that both legs of the bridge being assisted will receive the same auxiliary current. Although this requirement may lead to excessive currents in one leg of each of the linked converters, it can be successfully employed when used in combination with other ZVS methods. One such approach which synergizes well is the use of modified MCTs.
In this chapter, the use of PSM auxiliary legs for ZVS assistance will be focused on first. This approach provides the most flexible ZVS assistance and does not lead to excessive conduction losses due to larger than needed current if controlled properly. A hybrid approach using inductively linked converters to provide primary side ZVS and modified MCTs for secondary side ZVS is described next.
V.1 PSM Leg ZVS Assistance Modeling
The phase shift modulated halfbridge (PSMHB), also known as the auxiliary resonant pole (“ARP”) is one type of active softswitching assistance circuit specifically useful for maintaining zero voltage switching of half and fullbridge switch networks. Analysis of this method focuses first on a single pair of halfbridge switch networks linked through an inductor. Although specifically focusing on PSM auxiliary legs, much of the same analysis is applicable to inductively linked converters.
In one embodiment, the converter 10 may include an assisted ZVS apparatus 2300 with a first auxiliary switch Q_{1}′ connected to a positive connection of a switching leg of the converter 10. In
The assisted ZVS apparatus 2300 includes a second auxiliary switch Q_{2}′ connected between a negative connection of the switching leg and the first auxiliary switch Q_{1}′, Q_{2}′, where a connection point between the first and second auxiliary switches Q_{2}′ is an auxiliary midpoint V_{N}′. The assisted ZVS apparatus 2300 includes an auxiliary inductor L_{aux }connected between the auxiliary midpoint V_{N}′ and the main switch midpoint V_{N}. The main switch midpoint V_{N }is also connected to elements of the converter 10 in addition to the first and second main switches Q_{1 }and Q_{2 }and the auxiliary inductor L_{aux}.
The first and second main power switches Q_{1 }and Q_{2 }turn on and off as part of operation of the converter 10 and the first main switch Q_{1 }includes a first capacitance C_{N1 }and the second main switch Q_{2 }includes a second capacitance C_{N2}. In one embodiment, the first capacitance C_{N1 }and second capacitance C_{N2 }may be referred to as C_{N }and may be a same value. The assisted ZVS apparatus 2300 includes a switch regulation module 2302 that regulates switching of the first and second auxiliary switches Q_{1}′, Q_{2}′ to control current i_{aux }in the auxiliary inductor L_{aux}. The auxiliary inductor L_{aux }provides or removes charge from the first capacitance C_{N1 }and the second capacitance C_{N2 }to adjust voltage across the first main switch Q_{1 }and the second main switch Q_{2 }to induce zero voltage switching for the first and second main switches Q_{1}, Q_{2}.
In one embodiment, the first capacitance C_{N1 }is capacitance of the first main switch Q_{1 }and/or a capacitor connected in parallel with the first main switch Q_{1}. In addition, the second capacitance C_{N1 }is capacitance of the second main switch Q_{2 }and/or a capacitor connected in parallel with the second main switch Q_{2}. In another embodiment, the assisted ZVS apparatus 2300 includes a current sensing module 2304 that senses current i_{aux }in the auxiliary inductor L_{aux }and senses current i_{x }in the connection between the elements of the converter 10 and the main switch midpoint V_{N}. where the switch regulation module 2302 uses current sensed by the current sensing module 2304 and switching states of the first and second main switches to regulate switching in the first and second auxiliary switches to adjust current in the auxiliary inductor to adjust voltage across the first and second main switches Q_{1}, Q_{2 }to achieve zero voltage switching.
For a converter with switching period T_{s }and dead time t_{d}<<T_{s}, the approximate peak value of the auxiliary inductor current i_{aux}(t) can be written as a function of the phase shift between the main halfbridge and the auxiliary halfbridge Φ_{N},
Phase shift Φ_{N }is limited to angles between −π and +π, with maximum assistance current delivered at either limit. Positive and negative phase shifts are symmetric in terms of ZVS assistance under assumption (95), so that Φ_{N }can be constrained to the region between 0 and +π in order to simplify analysis without losing generality.
To ensure that ZVS is achieved across the full operating range of interest for Q_{1 }and Q_{2}, L_{aux }must be designed such that at maximum peak auxiliary current, with Φ_{N}=+π the worst case, switch node currents can be compensated for by i_{aux}(t). The converter of interest determines how the worst case switch node current is found, but for a general switch node current of i_{x}(t) with positive current needed to achieve ZVS, L_{aux }can be approximated with the inequality
where W_{x }is the operating region of interest over which the assisted converter (Q_{1 }and Q_{2}) will operate, and V_{A }is the bridge voltage as seen in
For L_{aux }satisfying (96), ZVS is possible at all operating points based on the phase angle Φ_{N}. Phase angles smaller than necessary lead to hard switching of Q_{1 }and Q_{2}, while phase angles larger than needed lead to excessively high conduction losses in L_{aux}, Q_{1}′, and Q_{2}′. In order to minimize the overall losses of the system, Φ_{N }must be regulated as close to its minimum value as possible while still producing the needed auxiliary assistance current peak. Beginning with the above analysis, this minimum value may be calculated directly.
To ensure complete soft transitions in the switch node voltage V_{N }from
Assuming that i_{aux}(t)≈i_{AUX }throughout the dead time simplifies the analysis, and after substituting (95) into (97) allows the control angle necessary for ZVS to be written as a function of known constants and unknown converter parameters,
Note that Φ_{N }ideally maintains the same value for both Q_{1 }and Q_{2 }regardless of λ, as i_{x}(t) is assumed approximately halfperiod antisymmetric such that λi_{x}(t) maintains the same sign for both Q_{1 }and Q_{2}.
All quantities in (99) are well known except for the integral of the converter current into the node over the dead time t_{d}. Although this value may be approximated well with various methods, it is hard to achieve the accuracy needed due to unmolded ringing and other effects. In order to avoid this issue, the left had side of (97) may be directly calculated with the use of an analog windowed integration circuit. The result of this analog integration is compared with a voltage dependent reference value equal to the right hand side of (97) to determine if more or less ZVS assistance is needed in order to softswitch Q_{1 }and Q_{2}. This method does not require knowledge of i_{x}(t), and uses a reference which is easily computed or found experimentally. For a constant V_{A}, the voltage dependent reference is constant and is used as the feedback reference variable when designing a feedback controller for ZVS assistance. The use of this constant feedback reference greatly simplifies controller implementations.
S_{a}=!(GD[Q_{1}]GD[Q_{2}]). (100)
The resulting output voltage of the windowed integration circuit 17, is a scaled representation of the integrated switch node current on the left side of (97)
Using (101) as the feedback variable, the right hand side of (97) is scaled accordingly to provide the feedback reference,
To avoid perturbations in the average auxiliary current, a modulation technique can be used that directly modifies the peaktopeak current without perturbing the average inductor current. One method that achieves this is ‘halfstepfirst’ modulation. Seen in
Using halfstepfirst phase angle updates, PSMHB phase modulation is analyzed as a completely digital system composed of a scaled delay of at most one switching period. The linearized small signal gain relating Φ_{N }and i_{AUX }is derived by differentiating (95) with respect to Φ_{N}. To simplify analysis, a constant single cycle delay for modulation is assumed. This will at worst cause control margins to be larger than expected, and is a reasonable assumption for many implementations of the phase modulator. The PSMHB transfer function can be defined with sample frequency f_{s }as
The current integration scheme described above can be analyzed as a sensor gain relating the switch node currents during the Q_{1}/Q_{2 }dead time and the total change delivered to the switch node as a scaled voltage. Assuming a capacitor C_{q }is used to integrate the node current, the current integration gain can be approximated as
using the circuit parameters defined in
The samples returned by the current integration circuitry alternate between the Q_{1 }and Q_{2 }device currents with a sample frequency of 2f_{s}. In poorly matched systems, this may cause oscillations between two values at the output of the current integrator even in steady state. The addition of a running two sample minimum block after the integrator safely solves this issue if needed, and can be acceptably modeled for most analysis by an additional single sample (one half switching period) delay added to (103). This has the additional effect of simplifying control loop analysis, as both (102) and a modified (103) have common sample rates off, after making this assumption.
T_{PSM}=C_{p}[z]H_{PSM}[z]A_{q}[z], (105)
although the closed loop transfer functions differ. For charge reference, the closed loop transfer function is derived as
while the closed loop disturbance transfer function becomes
The two transfer function found in (106) and (107) are the desired result, allowing feedback control of PSMHB ZVS assistance.
When ZVS assistance is not needed in the main converter, it is desirable to minimize the conduction losses in the auxiliary inductance added by the PSMHB assistance circuitry. By setting Φ_{N }to zero, PSMHB conduction losses may be eliminated, although such an approach causes PSMHB auxiliary devices to hard switch causing large switching losses especially at higher switching frequencies. A better approach is to maintain a minimum current in the PSMHB at all times, such that conduction losses are minimized while softswitching is maintained. To ensure this, a minimum control angle, Φ_{Min}, should be set such that
In (108), the PSM halfbridge switches are assumed to have an output capacitance of C_{A}, and a dead time of t_{dA}. By using devices with small output capacitance, and letting t_{dA }be relatively large, Φ_{Min }can be kept small resulting in a small i_{AUX }and reduced overhead losses when the main converter does not need ZVS assistance. This result is one argument for selecting PSMHB devices with small output capacitances. Unfortunately, small output capacitance MOSFET devices are likely to have larger onstate resistances making it unclear which parameter should be focused on in device selection.
To help clarify the situation, the RMS value of the minimum i_{aux}(t) needed based on (108) for PSMHB ZVS operation can be calculated as a function of circuit parameters,
As conduction losses are proportional to the square of (109), we can see that conduction losses are approximately proportional to the square of the output device capacitance. When compared with the linear relation between losses and onstate resistance, it becomes clear that PSMHB auxiliary devices with minimum output capacitance should be chosen over devices with smaller onstate resistance. Selecting devices in this way will reduce losses introduced by the use of PSMHB ZVS assistance.
When designed such that the maximum i_{AUX }needed is achieved at Φ_{N}=π, the RMS and peak currents handled by the PSMHB switching devices are in many cases much smaller than those handled by the main converter. For the best case design, the maximum RMS current handled by the PSMHB switching devices is
For many converters, this means that much smaller devices may be used for the PSMHB than for the main converter components as i_{AUX }is only equal to the peak worstcase current experienced by the main switches devices, not the total current handled by the main switching devices. Voltage stresses for both auxiliary devices and main switching elements will remain the same, while the power loss in the auxiliary switches will be significantly lower than the main switches due to the reduced currents they must handle. The lower power loss experienced by these devices allows less effort and space to be spent cooling the devices, reducing the additional volume the PSMHB auxiliary circuits require.
Based on the power stage designed in Section III.2 the charge integration circuit designed uses a 1:22 current sense transformer, loaded with R_{s}=40Ω. The opamp integrator uses R_{f}=1 kΩ and C_{q}=1 nF, resulting in a gain of approximately 0.7 V/A equivalent. No additional switch node capacitance was added to the main switching devices, such that the C_{A }and C_{N }are equal to the output capacitance of the MOSFET devices used. The charge references in (102) are experimentally derived and stored in a lookup table of values. Experimental derivation of the charge reference look up table was done due to the highly nonlinear nature of the output capacitance of a MOSFET device operated at variable voltage levels.
L_{aux}=80 01 was selected using available analytical models for the turn off currents of the DAB converter designed and (96), and then reduced slightly to give a small safety margin. Auxiliary switching devices use a dead time 10% larger than main switching devices, and were selected for lower output capacitance. Main switches used IRFP21N60L devices with an output capacitance of approximately 90 pF at 130V, while auxiliary devices (STW20N95K) had an output capacitance of approximately 40 pF at 130V.
In one embodiment, the first and second main switches Q_{1}, Q_{2 }form a first switching leg of a full bridge switching network of the converter 10 and the converter 10 includes a third main switch Q_{3 }connected to the positive connection of a second switching leg and a fourth main switch Q_{4 }connected to negative connection of the second switching leg. The first and second switching legs form a full bridge switching network. The embodiment also includes a third auxiliary switch Q_{3}′ connected to the positive connection of the second switching leg, a fourth auxiliary switch Q_{4}′ connected to a negative connection of the second switching leg, and a second auxiliary inductor L_{aux2 }connected to a second auxiliary midpoint V_{N2}′ between the third and fourth auxiliary switches Q_{3}′, Q_{4}′ and a second main switch midpoint V_{N2 }between the third and fourth main switches Q_{3}, Q_{4}, where the third main switch Q_{3 }includes a third capacitance C_{N3 }and the fourth main switch Q_{4 }includes a fourth capacitance C_{N4}. In the embodiment, the switch regulation module 2302 regulates switching of the third and fourth auxiliary switches Q_{3}′, Q_{4}′ to control current in the second auxiliary inductor L_{aux2}, where the second auxiliary inductor L_{aux2 }provides or removes charge from the third capacitance C_{N3 }and the fourth capacitance C_{N4 }to adjust voltage across the third main switch Q_{3 }and the fourth main switch Q_{4 }to induce zero voltage switching for the third and fourth main switches Q_{3}, Q_{4}.
In another embodiment, the converter 10 is a DABSRC converter 100, 101, the full bridge switching network is a first full bridge switching network on a primary side 141 of the converter 10 and the converter 10 includes a second full bridge switching network on a secondary side 143 of the converter 10 and each switching leg of the second full bridge switching network includes two auxiliary switches (i.e. Q_{1}′, Q_{2}′) and an auxiliary inductor (i.e. L_{aux}) controlled by a switch regulation module (i.e. 2302) to achieve zero voltage switching of switches (i.e. Q_{1}, Q_{2}) in the second full bridge switching network. In one embodiment, the assisted ZVS apparatus 2300 includes a ZVS activation module 2306 that activates switching of the first and second auxiliary switches Q_{1}′, Q_{2}′ and the switch regulation module 2302 when the converter 10 is in a hard switching condition.
V.2 PSM Leg ZVS Assistance Control
PSM auxiliary leg control relies on equations (105)(107) for design of a feedback controller. Unlike the main power flow control loop, the PSM control loop is independent of converter operating point, with only the voltage dependence of the charge reference (102) varying in response to the applied bridge voltage. Design of the charge reference to auxiliary current controller is done using digital integral controller. The controller gain K_{iZVS }selected in order to maintain a phase margin of P_{M}≧70° and a gain margin G_{M}≧10 dB. The resulting controller uses a gain of K_{iZVS}=100e3, with the closed loop control to output transfer function plotted in
The closed loop disturbance to auxiliary current is checked to ensure that the bandwidth is sufficiently large. As this transfer function determines the speed with which a PSM auxiliary leg operated at a fixed bridge voltage can respond to changes in tank current magnitudes, a bandwidth much larger than the converters main power flow bandwidth is needed. Referencing the gain schedule controller designed in Section IV.2 the maximum converter bandwidth is 2.76 kHz at M=1.2 and U_{CMD}=−0.5. The closed loop bandwidth of the loop relating PSM leg disturbance to auxiliary current is found to be approximately 6 kHz, which satisfies the requirement of being sufficiently larger than that of the main power flow.
Using the controller derived above, a charge reference table still needs to be derived. Dependent on both the bridge voltage V_{A }and the switch node capacitance C_{N }charge reference Q_{REF},
may be computed analytically or experimentally. When a large switch node capacitance is added external to switching device output capacitances, analytically computing (111) becomes the desired option, as only the direct dependence on node voltage V_{A }need be considered as all other parameters can be considered constant. For converter legs designed with no additional capacitance, such that C_{N }is equal to the nonlinear voltagedependent output capacitance of a single switching device, experimental derivation of (111) is preferred. As the converter designed in III.2 does not use external capacitance on any of the switch legs experimental derivation of Q_{REF }is preferred.
Deriving the voltage dependent charge reference table for feedback control of PSMHB ZVS assistance involves experimentally switching a single pair of main switches in a halfbridge configuration at an arbitrary power level where hard switching is experience and sweeping the bridge voltage from the minimum expected value to the maximum expected value. At each voltage level, additional current is driven into the switch node under test by increasing the auxiliary PSMHB phase control angle until ZVS is achieved. At this point the charge integration output is recorded. By correlating the bridge voltage with the output value of the charge integration circuit as seen in
Maintaining minimum current for PSM auxiliary circuitry softswitching requires maintaining a minimum phase shift in the auxiliary legs,
Due to the nonlinear voltage dependent nature of the PSMHB switching device output capacitance C_{A }an experimentally determined table is used for Φ_{Min}. This table is derived in a similar manner to the table for Q_{REF }as it is again dependent on bridge voltage alone.
V.3 ZVS Assistance with Modified MCTs in Inductively Linked Converters
When multiple converters operate together with parallel input or output active bridges, it becomes possible to inductively link the parallel half bridges of one converter with another in order to remove the need to additional PSMHB circuitry for either the primary of the secondary. This approach allows half of the main switches in each converter to soft switch by applying a phase shift between the two converters without the need to additional hardware. As this approach can only be used to force ZVS of half the main switching elements, it must be used in conjunction with a separate method in order to force ZVS of the other half of the main switching elements. One such method is to use modified MCT. When implemented together, soft switching of all devices can be achieved without the need to additional switching elements by pairing converters together. This section describes one way in which this approach can be implemented.
In one embodiment, the MCT control module 8306 includes one or more phase shift modulators 230 that control switching of the switches of the converter 10 by controlling a plurality of angles between switching legs of the converter 10, where each switching leg includes two switches connected in series between positive and negative connections to the switching leg. For example, the switches may be similar to the switches 105 of
Equation (71) can be restated as,
which when solved for solved for every P_{OUT}ε[−P_{OUT}^{MAX}, P_{OUT}^{MAX}], yields a parameterized curve v_{φ,MCT}(P_{OUT}) in the control space, referred to as the MCT. Within the fundamental approximation the MCT can be expressed in closed form and analyzed in detail; the properties of the MCT relevant to the discussion are here summarized:
Having defined the voltage conversion ratio M as
the MCT is a 2D curve lying on the φ_{DC}=180° plane in the stepdown case (M<1) or on the φ_{AB}=180° plane in the stepup case (M>1).
When M<1, the MCT involves the modulation of both angles φ_{AD }and φ_{AB}; similarly, when M>1 both angles φ_{AD }and φ_{DC }are modulated.
When M=1, the MCT reduces to a oneangle modulation in which angle φ_{AD}≦90° controls the active power flow, while φ_{AB}=φ_{DC}=180°. Such situation corresponds to the conventional oneangle modulation considered.
The MCT yields, by definition, the combination of angles which results in the minimum flow of reactive power Q. This means that departing from the MCT by a controlled amount allows to control the sign and magnitude of the reactive power flowing through the tank, and hence the reactive component of the tank current.
As an example, consider
The flat portions of the MCT extending inside region R_{1 }correspond to heavy load operating points for which the minimum current operation occurs at Q_{DC}>0. The power level at which they depart from the φ_{AB}=180° line represents the minimum power level at which deep hard switching of the output devices can be avoided using a oneangle modulation strategy.
It is worth observing, with this regard, that the conventional oneangle modulation trajectory, in which φ_{AB}=φ_{DC}=180° and angle −90°≦φ_{AD}≦90° is employed to modulate the power flow, necessarily enters the capacitive region R_{C }at light load for nonunity conversion ratios. In one embodiment, the offset includes a fixed offset from the MCT in the ZVS region. In another embodiment, the offset includes a variable offset from the MCT in the ZVS region. For example, the offset may decrease as output power P_{OUT }increases. In another example, the offset follows a trajectory similar to the ZVS trajectory shown in
Referring, for simplicity, to the M<1 case only, and with the following definitions:
and A_{ZVS }having the same active power but different amounts of reactive power can be achieved.
Closedform expressions for v_{φ,ZVS}(P_{OUT}, I_{ZVS}) can be derived under the fundamental approximation already invoked previously, resulting in
when U_{OUT}≦(1−M′^{2})^{1/2}, and
when U_{OUT}>(1−M′^{2})^{1/2}. Similar expressions can be derived for the stepup case.
Expressions (116) correspond to the curved branches of the trajectory, with the ± sign referring to the upper or lower branch respectively. These branches are characterized by the fact that the ZVS currents i_{D↓ }and i_{C↓ }of the output devices, defined as the instantaneous current outsourced by node D (or C) at the turnoff instant of the highside device Q_{7 }(or Q_{5}), are equal to I_{ZVS}. On the other hand (117) correspond to the flat portions of the trajectory. Over these operating points one has i_{D↓}=i_{C↓}>I_{ZVS }because a nonzero minimum inductive current is already present in the tank, as previously discussed in the context of the MCT. Quantity I_{ZVS,FP }defined in (115), represents the ZVS current at full power, and also the maximum ZVS current that can be achieved or exceeded over the entire active power range. Levels above I_{ZVS,FP }and up to (1+1/M)·I_{ZVS,FP }are possible, but over limited power intervals and at the expense of much larger tank RMS currents.
Trajectories (116) and (117), parameterized in terms of the normalized active power U_{OUT}=P_{OUT}/P_{OUT}^{MAX }and of the normalized ZVS current on the output side α=i_{ZVS}/I_{ZVS,FP}, induce the (P_{OUT}, Q)tov_{φ }mapping anticipated at the beginning of this section. It can be proven that (116) and (117) reduces to the expression of the MCT for I_{ZVS}=0, i.e. v_{φ,ZVS}(P_{OUT}, i_{ZVS}=0)=v_{φ,MCT}(P_{OUT}) for every P_{OUT}. As I_{ZVS }increases from 0 to the fullpower value, trajectories of the type v_{φ,ZVS }expand deeper and deeper into the inductive power region R_{1}, connecting the MRP to the MFP points by “circumventing” the capacitive power region R_{C}.
While the trajectory control approach described in the previous section allows to exploit the degrees of freedom provided by the multiangle modulation to achieve full ZVS of the output devices, it exposes input devices Q_{1 }. . . Q_{4 }and Q_{1}′ . . . Q_{4}′ to hard switching over certain power levels.
In one embodiment, the MCT control module 8306 includes a feed forward control loop. For example, the feed forward control loop may be as depicted in
In one embodiment the converter includes a second DABSRC stage as depicted in
Note that auxiliary capacitors C_{aux }have the only function of preventing any DC current from flowing through the auxiliary branches.
Observe that phase shifting the two DABSRC stages does not impact the trajectory control approach for output ZVS operation described above, as it relies on an additional degree of freedom, i.e. φ_{AA′}, which is independent of the control vector v_{φ}=v′_{φ}. Furthermore, at heavy load, where no auxiliary current is normally needed, the proposed technique would null I_{aux }by saturating at φ_{AA′}=0, therefore preserving the heavy load efficiency of the DABSRC stages.
In view of the behavior illustrated in
Since based on passive coupling, the described approach has the advantage of not requiring additional switching devices for ZVS assistance. It also allows the DC/DC unit of
The foregoing ZVS technique provides two degrees of freedom, namely I_{ZVS }and φ_{AA′}, which respectively allow a controller to independently adjust the turnoff current at the output and input side of the DABSRC stages. Although the work in this section focuses on the theory and openloop validation of the discussed ZVS technique, it is important to point out that both I_{ZVS }and φ_{AA′} can be adjusted by two independent feedback loops so as to maintain the input and output turnoff currents at the desired set points. To this end, note that sensing the tank current would give such ZVS assistance control loops all the required information: as for the output turnoff current, it is the reflected version of the tank current sampled at the turnoff instant of any of the output devices; as for the input turnoff current, it is the sum of the tank current and of the auxiliary current, which can be considered known from φ_{AA′} and L_{aux }via (118). Implementation of the trajectory control equations (116) and (117) in a computationally affordable form represents another design challenge currently under investigation.
VI FPGA Controller ImplementationAn FPGA based controller for the DABSRC has been designed based on the control analysis from previous sections. Implemented on a Virtex5 FPGA device and coded in Verilog Hardware Design Language, the controller implements a number of simplifications in order to allow the design to be implemented in a reasonable amount of space. The FPGA used has a 100 MHz system clock which is increased to 200 MHz using a clock doubling PLL and includes block RAM for the implementation of the needed lookup tables. The converter switching frequency is set by stepping down the 100 MHz system clock to 97.7 kHz, and allows for 10 bit resolution in all phase shift angles. The 10 ns timing resolution possible when using a 100 MHz system clock with 10 bit phase angle resolution means that a maximum error of 0.1% is introduced into phase control angles by the phase shift modulator. All sensing in done with 12 bits of precision and internal computations on sensed variables are performed with 12 bit resolution. The lower two bits of 12 bit internal signals are only removed by the phase shift modulator during the last step of gate drive signal generation. The 200 MHz clock is used to access block RAM and to clock multipliers and dividers and all other logic blocks except for those involved in the final phase shift modulator for gate drive signal generation.
VI.1 MCT Modulator
In order to operate the DABSRC along the MCTs derived in Section IV.1 the converter output command must be translated into the correct three angle control vector. Two approaches are possible, the first using lookup tables and the second involving online computation of control angels by directly implementing the equations in (74) and (75) for the standard MCT or in (116) and (117) for the modified MCT. Only the standard MCT calculation will be dealt with here, although only small extensions are needed in order to implement the modified MCT calculations.
Using lookup tables to determine MCT control angles requires a two dimensional table using both converter output command as well as converter conversion ratio as indexes. Assuming that the converter conversion ratio is quantized as a 12 bit number K_{M }and that the converter output command is a 12 bit number K_{UCMD }which describes the full range of power outputs, a table for each control angle may be assembled with indexes of N_{M}≦K_{M }and N_{UCMD}<K_{UCMD }for conversion ratio and output command respectively. Assuming N_{φ }bits are used to represent control angles, the total table size Q_{MCT }can be calculated as
Q_{MCT}=3(2^{(N}^{M}^{+N}^{UCMD}^{+N}^{φ}^{)}). (119)
In order to keep the total storage size below 1−Mb for reasonable storage on an FPGA without external memory, a combined bit width N=N_{M}+N_{UCMD }N_{φ }of less than 18 bits is required. If only a few conversion ratios are needed, then this approach becomes acceptable, although in general the errors introduced with this method are unacceptable if storage size is kept within reasonable limits. For these reasons, a direct computation of the MCTs based on (74) and (75) is preferable.
Because of the complexity of (74) and (75) simplification is useful before implementation on the FPGA. To increase the symmetry of the MCTs, a new variable G,
is introduced. This simplification reduced the three MCT trajectories of interest to
Comparing φ_{AB }in (121) with φ_{DC }in
(123) and φ_{DC }in (121) with φ_{AB }in
(123) shows that a further simplification can be made by defining offangle φ_{PS }
φ_{PS}=2π−2 arcsin(√{square root over (G^{2}+(U_{OUT})^{2})}) (124)
partial main angle φ_{X},
temporary angle φ_{y }
φ_{y}=arcsin(U_{OUT}) (126)
and trajectory selection flag Q
Combining (124) and (127) with (121)(123) results in simplified equations for each of the three control angles,
Divisions and multiplications by 2 in (128)(130) can be accomplished using bit shifts, while G^{2 }and U_{CMD}^{2 }can be computed using either a multiplier or a look up table. The same lookup table may be used for both quantities by taking the magnitude and bit shifting U_{CMD }before referencing the table. Using multipliers requires less space in general, and can again be accomplished with a single element for both G^{2 }and U_{CMD}^{2}. To avoid computation of both an arctangent and an arcsine, the arctangents in (128)(130) are computed using the identity
which requires a squaring function, a square root function, and an arcsine function. With this substitution, only a square root and an arcsine remain to be computed. Fortunately the CORDIC algorithm allows computation of these two functions digitally on an FPGA. All functions generated by a CORDIC are possible to generate using look up tables, multipliers, or power series implementations, although in general a CORDIC implementation will allow for higher accuracy in less space.
In the prototype hardware built, computation of MCT angles is done without time multiplexing such that minimum time is taken to compute a new set of phase angles from output command and conversion ratio. This implementation requires a total of five multipliers, three dividers, and six CORDIC blocks. All computations use 12 bits, with operations resulting in 24 bits such as multiplication truncated back to twelve before further computations are performed.
VI.2 Gain Scheduled Feedback Controller
In order to generate the output command on which the MCT calculation acts, a digital integral controller is used. This controller includes a variable gain block in order to implement the gain scheduling scheme derived in Section IV.2.
The desire continuous time controller from Section IV.2 is transformed into discrete time using the forward rectangular rule,
By sampling the average output current at the switching frequency f_{s}=1/T_{s}=100 kHz errors introduced by this method of conversion are kept to a minimum. The resulting feedback equation for error signal e(k) and control output U(k) becomes
U[k+1]=T_{s}K_{i}e[k]+U[k]. (133)
For a given discrete gain K_{i}^{Disc}=T_{s}K_{i}, two constant integers K_{A }and K_{B }are selected such that
In this way, only integer multiplication and rightshifts are needed to generate fractional gains. A MATAB script is used to select the appropriate parameters K_{A }and K_{B}, which are stored in two dimensional lookup tables on the Virtex5. Bitwidths for K_{A }and K_{B }are selected using a script to minimize the error between K_{i}^{Disc }and the ideal gain for each operating point. This is done is such a way that the resulting discrete gain is never larger than its equivalent ideal gain to ensure that stability margins are maintained. Each cycle, the current operating point is recalculated based on a running average of the last eight samples for both current and voltage. Based on this average operating point, a new gain is selected for the controller every switching cycle using conversion ratio and output command to index into the precomputed K_{A }and K_{B }lookup tables.
VI.3 PSM Leg ZVS Assistance Controller
The PSM leg ZVS controllers are implemented based on the results of Section V.2. This design requires an integral controller and the use of two look up tables for storing both the minimum phase shift angle for ensuring auxiliary leg soft switching as well as the voltage dependent charge reference for ensuring main leg ZVS transitions as seen in
Each PSMHB leg operates independently from the rest, requiring four individual integral controllers. For each main leg, measurements of the charge delivered into the main switch node are taken twice a switching cycle at both the main switch leg rising transition and falling transition. Ideally the two returned values are equal in magnitude but of opposite sign. Due to nonidealities, small variations exist and so the minimum of the absolute value of the two measurements it taken. This 12 bit value is then subtracted from the needed charge reference provided by a bus voltage dependent lookup table and multiplied by the integral gain derived in Section V.2 using a 12 bit multiplier. The same integral controller setup seen in VI.2 is then used.
Each switching cycle a new minimum phase shift angle is determined using a lookup table based on the measured bus voltage. This minimum phase shift is applied to both the output of the integral controller block as well as to the stored previous state. In addition to this variable minimum output, a maximum output corresponding to a π degree phase shift is applied.
The two lookup tables used for ZVS operation are stored in the same manner using two port block RAM on the FPGA device. To minimize table size, the stored values are first level shifted such that the minimum value stored is zero. This reduces the number of bits needed for each charge reference or minimum angle but requires the level shift offset to be reapplied before the values are used as seen in
Using two port block RAM allows both the primary and secondary pairs of PSM half bridges to index using the possibly different primary and secondary bus voltages without regard for timing considerations as seen in
VI.4 MultiMode Control
Multimode control of the DABSRC is implemented using power, voltage, and current references. Each of these references is represented as a signed 12 bit number scaled to be between −1 and 1. Using these set points, as well as the measured and averaged converter output voltage and current, the multimode controller generates a current reference used as an input for the gainscheduled feedback controller.
The integral controller designed in Section IV.3 and seen in (94) is implemented on the FPGA controller as a direct form I cascaded controller by cascading two single pole controllers. Each single stage is implemented in the same way as described here and as seen in
The input signal to each stage is initially multiplied by a 12 bit gain b_{0 }resulting in a 24 bit signal. The saved previous state is stored as a 22 bit number, which when multiplied by a 12 bit gain a_{0 }results in a 34 bit signal. After zero extending the 24 bit scaled error, these two quantities are summed and then downsized with saturation into a 22 bit result. This result is next saturated to the magnitude of the converter current reference and sent out of the stage as well as stored as the saved previous state. This method for saturating the voltage and power outer loop controllers results in smooth mode transitions. This removes the requirement for complicated mode transition logic and greatly simplifies the overall digital design. The output from these pairs of cascaded controllers is a current reference needed for regulation of either power or voltage.
Error signals for power and voltage control are generated separately using error generation modules. A current reference error signal is not necessary, as saturation is used to enforce the current limit as seen in Section IV.3. Droop is added to the current reference using a 12 bit multiplier before being used to saturate the voltage and power controllers.
Two separate voltage errors are derived in the multimode controller as seen in
In order to verify the analytical results from the previous sections, a number of simulation models of varying accuracy have been developed. Beginning with a full switching model including tank losses and component nonidealities implemented in LTSpice, the models increase in simulation speed and decrease in complexity up to a system level model useful for analyzing a MMC DABSRC as part of a larger power system.
VII.1 Switching Level Models
Switching level models of the DABSRC are designed using a spice simulator. These models provide the highest level of accuracy with respect to hardware. Using simulation models provided by device manufacturers, the effect of different switching devices can be evaluated. Other nonidealities include transformer coupling and stray capacitance/inductance, resonant capacitor ESR and tank component mismatch, switching component on resistance, as well as switch node capacitance.
A full model of the DABSRC including four ZVS assistance legs has been developed. This model uses static control angles to investigate the operation of the DABSRC at the desired operating point. Although extremely accurate, a switching level model of this accuracy takes a large amount of time to run.
VII.2 Approximated Switching Level Models
To reduce the simulation time of a full switching level model, approximated switching models are designed in Simulink using the PLECS block set for power electronics. These models remove many of the nonidealities present in a full switching simulation and allow the model to directly interface with the MATLAB environment.
The approximated switching level model developed uses a simplified tank design with a single capacitor and a single inductor. An ideal tank transformer is used to further reduce simulation complexity. Tank losses are approximated with a lumped resistor element, in order to maintain the needed Q factor of the resonant tank. By using ideal switching elements, simulation time is further reduced. Switch nodes include no capacitance, either external or internal to switching elements. This reduces the order of the simulation and provides the greatest increases in speed.
The approximated switching model includes a phase shift modulator in order to generate phase shift control signals for the DABSRC. This model assumes no quantization error on PWM outputs, and provides timing resolutions of the selected simulation time step for all reasonable values. Finally, an MCT calculation block may be included, allowing the DABSRC to be controlled along the MCT by using an output command, U_{CMD }to set phase angles.
VII.3 Small Signal Models
The small signal models of Section III.3 are easily implemented in MATLAB and allow simplified controller design. Additionally they may be directly compared with the approximated switching level model of Section VII.2 in order to verify their accuracy.
All small signal models are stored in state space form in MATLAB due to the reduced accuracy that a transfer function representation results in for high order models such as those describing the DABSRC. All quantities are stated in terms of the input voltage and conversion ratio, such that output voltage is not directly known in the simulation environment. This allows all quantities to be scaled by the input voltage, providing models which are independent of voltage, and only depend on conversion ratio and power level.
VII.4 System Level Models
In order to test the DABSRC as a component of a larger power system, a system level model was developed. This model describes a variable number of DABSRC stages connected together to form a converter module. In addition, the multimode controller (MMC) used to provided power, voltage and current limits is modeled to match FPGA implementations as closely as possible without over complicating the simulations.
Two versions of this model have been designed and tested. The first contains a continuous controller model of the MMC, while the second is a mixed signal model using a digital controller implementation. Both models are interchangeable and configured the same way, although the mixed signal version generally simulates faster. Both implementations represent the DABSRC as a current source with a bandwidth determined by the gain scheduled controller. In general this allows the DABSRC to function as a first order low pass filter with a pole at the desired converter bandwidth. ZVS assistance circuitry is ignored for this model, as the control loops involved have no effect on the overall system.
As the prototype hardware built uses a small microcontroller in order to interface between a module of multiple DABSRC stages and a control computer, the system level model includes an approximation of this interface. This portion of the model allows the system to be interacted with in the same way and with the same commands as the physical hardware would be. Saturation and quantization caused by the microcontroller interface are included when needed.
In order to allow for arbitrary loads connected to the output of the DABSRC module, the output voltage is fed as an input into the converter model. This allows either a further simulation model or transfer function to determine the relation between converter output current and voltage. To test this functionality, a switched load was developed which models constant power, voltage, resistance, or capacitance.
Finally, the system level model uses experimentally collected efficiency data in order to estimate the system efficiency at any operating point. This is done using a table of efficiency measurements from a single DABSRC prototype, and interpolating between points in order to approximate system efficiency.
VIII Experimental VerificationExperimental verification was carried out using the converter designed in Section III.2. Two identical prototype converters were designed for verification so that converter interconnection could be studied. Analytical results in this chapter are compared with the models developed in Section VII, while experimental results are generated with prototype converters running the controllers designed in Section V.
VIII.1 Prototype Converter
Prototype converters were designed using four layer PCBs with equal layer spacing and 2 OZ copper traces. Shielded differential pair connections are used to connect each converter to its controller FPGA. Hand wound inductors are used for both auxiliary and tank components. The isolation transformer was designed and assembled offsight. Each converter includes an oversized EMI filter on both the input and output terminals. 10 kV isolation is achieved between both primary and secondary sides of the converter. Additionally, 10 kV isolation between the controllers and the converters is included. A bank of fans is used to cool the converters, which are enclosed either in an acrylic or metal case for safety and transport. Thermocouple sensors are attached to both the primary and secondary main switching elements in order to monitor device temperatures. For safety and converter protection, over voltage shutoff circuitry is included on both the primary and secondary voltage busses.
VIII.2 Small Signal Models
The transfer functions from Section III.3 can be verified both in simulation and hardware. Mathematica was used for all transfer function calculations, while MATLAB was used to plot step and frequency responses. A tank Q factor of 25 was used for simulation.
Initial verification of converter transfer functions was done by examining the step response of the tank current with respect to changes in control angle.
Additional verification was done by introducing a sinusoidal signal of known frequency and magnitude onto each control angle, and examining the Fast Fourier Transform (“FFT”) of the tank current and the output current at a variety of frequencies. These points are then compared to plots of the expected frequency response. As the response of the DABSRC varies with DC operating point, these experiments were carried out at a variety of steady state locations.
with Φ_{DC}=180°, and Φ_{AD}=90°.
with Φ_{AB}=180°, and Φ_{DC}=180°. Experimental data in circles for ±4° perturbations are plotted on top of derived response at 3.125 kHz, 6.25 kHz, 12.5 kHz, 25 kHz, and 50 kHz.
with Φ_{AB}=180°, and Φ_{AD}=90°.
Output current magnitude responses are plotted in
VIII.3 Verification of the MCTs
The simulation model described in Section VII.2 set up in order to simulate the foregoing design and investigate how closely the analysis describes the behavior of the DABSRC stage. The two major effects accounted for by the simulations and not considered by the theoretical analysis are the nonsinusoidal nature of the voltage and current waveforms, and a nonzero dead time t_{d}. The model simulates the DABSRC in openloop conditions with a programmable control vector v_{φ}, allowing simulation of an arbitrary point in the control space C_{s}. Case M=0.5 is exemplified in this section, obtained by setting V_{OUT}=200 V. Note that the maximum available power is in this case halved with respect to the nominal rating, according to (32). A first set of simulations was performed along the theoretical minimum current trajectories in the [−P_{OUT}^{MAX}, P_{OUT}^{MAX}] range, sweeping the operating point from the MRP to the MFP point; the positive branch γ_{1+} of the MCT was chosen as the minimum current path over the P_{OUT}/P_{OUT}^{MAX}≦(1−M^{2})^{1/2 }power range.
As anticipated in Section IV.1, when the oneangle modulation is adopted, the output bridge experiences severe hardswitching losses below the critical power P_{OUT}/P_{OUT}^{MAX}=(1−M^{2})^{1/2}. Overall, one can observe how ZVS operation of the output bridge along the conventional oneangle trajectory would require the injection of a strong inductive current into the switching nodes D and C, e.g. through some auxiliary ZVS circuitry provision. On the other hand, a much reduced auxiliary current would be required when operating the DABSRC along the MCT. Similarly, a small amount of inductive current would be required at the input side to achieve full ZVS operation. Overall, the MCT strongly reduces the criticalities in designing ZVS assistance provisions. These observations confirm the theoretical importance of the minimum current operation and open the possibility to more advanced trajectory control approaches that, taking the MCT theory as a starting point, aim at improved ZVS and efficiency optimization.
A 1 kW DABSRC prototype was employed in experimental tests described below, where 600 V, 13 A power MOSFETs IRFP21N60L were been employed as electronic switches. The operating control vector v_{φ }is set from a PC via a custommade Graphic User Interface communicating with the FPGA device via a serial link. For the sake of definiteness, in what follows the output power P_{OUT }is always intended as the power delivered to the output source V_{OUT }and measured at the corresponding port.
The DABSRC prototype was first tested at nominal input and output voltages (M=1), using a 500 V DC power supply and an electronic load programmed in constant voltage mode and set to 400 V. The setup was employed for both forward and reverse power tests by exchanging the DC supply and the electronic load accordingly. The power command was swept by adjusting angle φ_{AD }while maintaining φ_{AB}=φ_{DC}=180°. Since M=1, such oneangle modulation also represents the minimum current trajectory.
Next, the DABSRC prototype was tested at different control angles spanning a region of the φ_{DC}=180° plane with the purpose of experimentally constructing the power and current contours. In order to maintain a safe operation of the DABSRC stage where no large circulating currents could damage the hardware, such tests were performed at V_{IN}=200 V input and V_{OUT}=80 V output, corresponding to 100 W maximum power and M=0.5.
Operation of the DABSRC stage along the MCT was then compared with the simpler oneangle modulation. To this end, the stage was again tested at 200 V input/80 V output (M=0.5) along the two different trajectories.
Advantages of operating the converter on the MCT become of critical importance at higher power levels.
In light of the foregoing experimental tests and as anticipated in Section IV.1, operation along the MCT can serve as a starting point to minimize the effort required by auxiliary ZVS circuitry to optimize efficiency.
VIII.4 PSM Leg Functional Verification
Soft start transients were taken with a bridge voltage of 130 V.
At a slightly lower power level (600 mA forward power), the PSMHB feedback loop begins to regulate a larger phase angle in order to maintain ZVS of the main switching devices.
Further reducing the converter power level causes the PSMHB feedback loop to continuously modify Φ_{N }in order to maintain ZVS.
VII.5 Hybrid ZVS Assistance Verification
Experimental results for hybrid ZVS assistance were taken by connecting prototype converters as seen in
A more extensive bidirectional power sweep was performed along the conventional oneangle trajectory and along a ZVS trajectory. In the latter case, angle φ_{AA′} was manually adjusted so as to ensure a turnoff current of at least 1 A on the input side, while the control vectors v_{φ}=v′_{φ }were swept along the analytical curves of (116) and (117), evaluated at α=0.6 and corresponding to I_{ZVS }0.73 A theoretical output turnoff current.
VIII.6 Gain Scheduled Controller
VIII.7 MultiMode Controller
In order to test both power sharing as well as mode transitions, the multimode controller designed in Section IV.3 was simulated and tested experimentally using two converters with both series and parallel output connections. For simulation results the system level model from Section VII.4 is used. The simulation is setup with two separate converters, one with an output current regulation bandwidth of 2 kHz (converter A), and the other with an output current regulation bandwidth of 1 kHz (converter B) in order to show the effects of mismatched controllers on power sharing. Both converters operate with an output capacitance of 10 Voltage and power regulation outer loops are designed for bandwidths of 400 Hz for both converters.
Simulation models are setup with two converters operating with series output connection for current regulation test. The converters are loaded with a 10 kΩ resistor in parallel with a 100 μF load capacitance. The simulation begins with each converter output capacitor at 100 V and the load capacitor at 200 V. Both converters have a 2 A current limit and a 750 W power limit. A 250 V output voltage limit is set on both converters in order to achieve a total of 500 V output.
Simulation models are setup with two converters operating in parallel output connection for voltage regulation tests. As before, each converter is loaded with 10 μF of output capacitance. The converters are loaded with a 1 kΩ resistor. The simulation begins with 100 V across the output capacitance of the converter modules. Both converters have a 500 V output voltage limit and a 750 W power limit. A 1 A output current limit is set for each converter in order to achieve 2 A total output current.
Each of the three possible controller transitions was tested in simulation using the same models that were used to test power sharing during voltage and current regulation. For all tests, both converters have 10 μF output capacitors.
Current to power regulation transitions were verified using two converters operating with parallel output connections. Each converter operates with a 1 A output current limit for a total of 2 A output current and a 500 V output voltage limit. Converter A is uses a power limit of 196 W while converter B uses a power limit of 200 W in order to allow both output powers to be seen on the same plot. In order to force a current to power regulation transition, a variable load resistor of 100Ω to 400Ω is used.
Power to voltage regulation transitions were verified using two converters operating with series output connections. A load variable resistance loads the converter pair, is parallel with a 10 μF load capacitance. Both converters operate with a 2 A output current limit, a 375 W output power limit, and a 250 V output voltage limit for a total of 500 V output voltage. Initially, a 240Ω load resistor is used. After the startup transient, both converters are seen to operate in power regulation mode at 375 W in
Current to voltage regulation transitions were verified using two converters operating with parallel output connections. Each converter operates with a 1 A output current limit for a total of 2 A output current, a 500 V output voltage limit, and a 750 W output power limit. In order to force a current to voltage regulation transition, a variable load resistor of 100Ω to 400Ω is used.
The method 8000 controls 8006 output power P_{OUT }of the converter 10 to the negative power reference −P_{SET }over a constant power range between output voltage V_{OUT }of the converter 10 being at the output voltage reference V_{SET }and a maximum negative power limit of the converter 10. The method 8000 limits 8008 output current I_{OUT }to a positive output current reference I_{SET }in a range between a minimum output voltage and output power P_{OUT }of the converter reaching the positive power reference P_{SET}, and the method 8000 ends.
If the method 8100 determines 8106 that the output power P_{OUT }has not reached the positive power reference P_{SET }and that the output current I_{OUT }is below the positive output current reference I_{SET}, the method 8100 determines 8110 if output power P_{OUT }is between a positive power reference P_{SET }and a negative power reference P_{SET }and if the output current I_{OUT }is less than an output current reference I_{SET}. If the method 8100 determines 8110 that the output power P_{OUT }is between a positive power reference P_{SET }and a negative power reference P_{SET }and that the output current I_{OUT }is less than an output current reference I_{SET}, the method 8100 controls 8112 output voltage V_{OUT }to the output voltage reference V_{SET}.
If the method 8100 determines 8110 that the output power P_{OUT }is not between a positive power reference P_{SET }and a negative power reference P_{SET }or that the output current I_{OUT }is not less than an output current reference I_{SET}, the method 8100 determines 8114 if the output power P_{OUT }has reached the negative power reference P_{SET }and if the output power P_{OUT }is below a maximum negative power limit. If the method 8100 determines 8114 that the output power P_{OUT }has reached the negative power reference −P_{SET }and that the output power P_{OUT }is below a maximum negative power limit, the method 8100 controls 8116 output power P_{OUT }to the negative power reference −P_{SET}. The method 8100 returns and continues to monitor output power P_{OUT}, output current I_{OUT}, and output voltage V_{OUT }against the setpoints and limits described above.
The method 8200 may use the current i_{aux }sensed 8204 in the auxiliary inductor L_{aux }and current i_{x }in the connection between the elements of the converter 10 and the main switch midpoint V_{N }and may use switching states of the first and second main switches Q_{1}, Q_{2 }to regulate 8206 switching in the first and second auxiliary switches Q_{1}′, Q_{2}′ to adjust current i_{aux }in the auxiliary inductor to adjust voltage across the first and second main switches Q_{1}, Q_{2 }to achieve zero voltage switching. In another embodiment, regulating 8206 switching of the first and second auxiliary switches Q_{1}′, Q_{2}′ may include controlling current i_{aux }in the auxiliary inductor L_{aux }by controlling a phase angle Φ_{N }between a voltage transition at the auxiliary midpoint and the main switch midpoint.
The method 8600 adjusts 8608 current a link between linked DABSRC stages to control ZVS in one or more switching legs. For example, the converter 10 may include linked DABSRC stages as depicted in
The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.
Claims
1. An apparatus comprising: Φ N ≥ 4 π f s L aux t d ( 2 C N  λ V A ∫ t d i x ( t ) ⅆ t )
 a first auxiliary switch connected to a positive connection of a switching leg of a direct current (“DC”) to DC converter, the switching leg comprising a first main switch and a second main switch, the first and second main switches connected at a main switch midpoint;
 a second auxiliary switch connected between a negative connection of the switching leg and the first auxiliary switch, wherein a connection point between the first and second auxiliary switches comprises an auxiliary midpoint;
 an auxiliary inductor connected between the auxiliary midpoint and the main switch midpoint, the main switch midpoint further connected to elements of the converter in addition to the first and second main switches and the auxiliary inductor, wherein the first and second main power switches turn on and off as part of operation of the converter, the first main switch comprising a first capacitance and the second main switch comprising a second capacitance; and
 a switch regulation module that regulates switching of the first and second auxiliary switches to control current in the auxiliary inductor, the auxiliary inductor providing or removing charge from the first capacitance and the second capacitance to adjust voltage across the first main switch and the second main switch to induce zero voltage switching for the first and second main switches, wherein the switch regulation module controls current in the auxiliary inductor by controlling a phase angle between a voltage transition at the auxiliary midpoint and the main switch midpoint, and wherein the switch regulation module controls the phase angle according to the equation:
 where ΦN is the phase angle between the voltage transition at the auxiliary midpoint and the main switch midpoint; fs is the switching frequency of the converter; Laux is inductance of the auxiliary inductor; td is a dead time between switching of the first main switch and the second main switch; CN is capacitance of one of the first capacitance and the second capacitance; VA is voltage of the power source; ix (t) is current in the connection between the elements of the converter and the main switch midpoint; and λ is +1 when the first main switch is on and −1 when the second main switch is on.
2. The apparatus of claim 1, wherein the first capacitance comprises one or more of capacitance of the first main switch and a capacitor connected in parallel with the first main switch, and wherein the second capacitance comprises one or more of capacitance of the second main switch and a capacitor connected in parallel with the second main switch.
3. The apparatus of claim 1, further comprising a current sensing module that senses current in the auxiliary inductor and in the connection between the elements of the converter and the main switch midpoint, wherein the switch regulation module uses current sensed by the current sensing module and switching states of the first and second main switches to regulate switching in the first and second auxiliary switches to adjust current in the auxiliary inductor to adjust voltage across the first and second main switches to achieve zero voltage switching.
4. The apparatus of claim 1, wherein the converter comprises a resonant power converter.
5. The apparatus of claim 4, wherein the resonant power converter comprises at least one stage of a dual active bridge series resonant converter (“DABSRC”).
6. The apparatus of claim 1, wherein the first and second main switches comprise a first switching leg of a full bridge switching network of the converter, wherein the converter comprises a third main switch connected to the positive connection of a second switching leg and a fourth main switch connected to negative connection of the second switching leg, the first and second switching legs forming a full bridge switching network, and further comprising:
 a third auxiliary switch connected to the positive connection of the second switching leg;
 a fourth auxiliary switch connected to a negative connection of the second switching leg; and
 a second auxiliary inductor connected to a second auxiliary midpoint between the third and fourth auxiliary switches and a second main switch midpoint between the third and fourth main switches, the third main switch comprising a third capacitance and the fourth main switch comprising a fourth capacitance,
 wherein the switch regulation module regulates switching of the third and fourth auxiliary switches to control current in the second auxiliary inductor, the second auxiliary inductor providing or removing charge from the third capacitance and the fourth capacitance to adjust voltage across the third main switch and the fourth main switch to induce zero voltage switching for the third and fourth main switches.
7. The apparatus of claim 6, wherein the converter comprises a DABSRC converter, wherein the full bridge switching network comprises a first full bridge switching network on a primary side of the converter and further comprising a second full bridge switching network on a secondary side of the converter and wherein each switching leg of the second full bridge switching network comprises two auxiliary switches and an auxiliary inductor controlled by a switch regulation module to achieve zero voltage switching of switches in the second full bridge switching network.
8. The apparatus of claim 1, wherein the switch regulation module operates independent of feedback control loops of the converter.
9. The apparatus of claim 1, further comprising a ZVS activation module that activates switching of the first and second auxiliary switches and the switch regulation module when the converter is in a hard switching condition.
10. The apparatus of claim 1, wherein the converter comprises a DABSRC converter comprising a current feedback loop, wherein the current feedback loop further comprises compensation implemented using a gain scheduled feedback controller, the gain scheduled feedback controller comprising one or more output control signals that vary over a plurality of control regions, the gain scheduled feedback controller implementing a different compensation equation for each control region.
11. The apparatus of claim 10, wherein the converter comprises one or more phase shift modulators controlled by the one or more output control signals, wherein the one or more output control signals control according to a minimum current trajectory (“MCT”) control technique, the MCT substantially minimizing circulating current within the converter.
12. The apparatus of claim 10, wherein the gain scheduled feedback controller maintains at least a portion of the main switches of the converter in a zerovoltage switching (“ZVS”) region while minimizing circulating current by following a trajectory a fixed distance from an MCT for a portion of operating regions of the converter and the switching regulation module controls auxiliary switches connected to at least a portion of the main switches of the converter to maintain zero voltage switching when the main switches connected to the auxiliary switches operate in a hard switching operating region.
13. A system comprising: Φ N ≥ 4 π f s L aux t d ( 2 C N  λ V A ∫ t d i x ( t ) ⅆ t )
 a direct current (“DC”) to DC converter comprising one or more switching legs, each switching leg comprising two main switches connected at a main switch midpoint wherein a first main switch of the switching leg is connected between a positive connection of the switching leg and the main switch midpoint and a second main switch of the switching leg is connected between the main switch midpoint and a negative connection of the switching leg, wherein each switching leg comprises a portion of one of a half bridge switching network and a full bridge switching network; and
 an assisted zero voltage switching (“ZVS”) apparatus connected to one or more switching legs of the converter, each ZVS apparatus of a switching leg comprising a first auxiliary switch connected between an auxiliary midpoint of the switching leg and the positive connection of the switching leg; a second auxiliary switch connected between the auxiliary midpoint and the negative connection of the switching leg; an auxiliary inductor connected between the auxiliary midpoint and the main switch midpoint of the switching leg, the main switch midpoint connected to elements of the converter in addition to the first and second main switches of the switching leg, wherein the first and second main power switches turn on and off as part of operation of the converter, the first main switch comprising a first capacitance and the second main switch comprising a second capacitance; and a switch regulation module that regulates switching of the first and second auxiliary switches to control current in the auxiliary inductor, the auxiliary inductor providing or removing charge from the first capacitance and the second capacitance to adjust voltage across the first main switch of the switching leg and the second main switch of the switching leg to induce zero voltage switching for the first and second main switches, wherein the switch regulation module controls current in the auxiliary inductor by controlling a phase angle between a voltage transition at the auxiliary midpoint and the main switch midpoint, and wherein the switch regulation module controls the phase angle according to the equation:
 where ΦN is the phase angle between the voltage transition at the auxiliary midpoint and the main switch midpoint; fs is the switching frequency of the converter; Laux is inductance of the auxiliary inductor; td is a dead time between switching of the first main switch and the second main switch; CN is capacitance of one of the first capacitance and the second capacitance; VA is voltage of the power source; ix (t) is current in the connection between the elements of the converter and the main switch midpoint; and λ is +1 when the first main switch is on and −1 when the second main switch is on.
14. The system of claim 13, further comprising an electronic device powered by the converter.
15. A method comprising: Φ N ≥ 4 π f s L aux t d ( 2 C N  λ V A ∫ t d i x ( t ) ⅆ t )
 regulating switching of a first auxiliary switch and a second auxiliary switch to control current in an auxiliary inductor, the auxiliary inductor providing or removing charge from a first capacitance of a first main switch of a switching leg and a second capacitance of a second main switch of the switching leg to adjust voltage across the first main switch and the second main switch to induce zero voltage switching for the first and second main switches, the switching leg comprising a portion of a direct current (“DC”) to DC converter, wherein the first and second main power switches turn on and off as part of operation of the converter,
 wherein the first auxiliary switch is connected to a positive connection of the switching leg and to an auxiliary midpoint; the second auxiliary switch is connected between the auxiliary midpoint and a negative connection of the switching leg; the auxiliary inductor is connected between the auxiliary midpoint and a main switch midpoint, the main switch midpoint comprising a connection between the first main switch and the second main switch, the main switch midpoint connected to elements of the converter in addition to the first and second main switches and the auxiliary inductor and controlling current in the auxiliary inductor comprises controlling a phase angle between a voltage transition at the auxiliary midpoint and the main switch midpoint, and wherein the switch regulation module controls the phase angle according to the equation:
 where ΦN is the phase angle between the voltage transition at the auxiliary midpoint and the main switch midpoint; fs is the switching frequency of the converter; Laux is inductance of the auxiliary inductor; td is a dead time between switching of the first main switch and the second main switch; CN is capacitance of one of the first capacitance and the second capacitance; VA is voltage of the power source; ix (t) is current in the connection between the elements of the converter and the main switch midpoint; and λ is +1 when the first main switch is on and −1 when the second main switch is on.
16. The method of claim 15, further comprising sensing current in the auxiliary inductor and in the connection between the elements of the converter and the main switch midpoint and wherein regulating switching of the first and second auxiliary switches further comprises using the current sensed in the auxiliary inductor and in the connection between the elements of the converter and the main switch midpoint and using switching states of the first and second main switches to regulate switching in the first and second auxiliary switches to adjust current in the auxiliary inductor to adjust voltage across the first and second main switches to achieve zero voltage switching.
17. The method of claim 15, wherein regulating switching of the first and second auxiliary switches further comprises controlling current in the auxiliary inductor by controlling a phase angle between a voltage transition at the auxiliary midpoint and the main switch midpoint.
18. The method of claim 15, wherein the switching leg comprises a first switching leg of the converter and wherein the converter comprises additional switching legs and further comprising regulating switching of first and second auxiliary switches to control current in an auxiliary inductor associated with each additional switching leg to achieve zero voltage switching in the main switches of each additional switching leg.
5546294  August 13, 1996  Schutten 
6072362  June 6, 2000  Lincoln 
6351401  February 26, 2002  Scheel 
6574125  June 3, 2003  Matsukawa 
7679337  March 16, 2010  Yoshida 
8031495  October 4, 2011  Sachdeva 
8492926  July 23, 2013  Collins 
8970161  March 3, 2015  Cuadros 
20050279298  December 22, 2005  Degner 
20100246231  September 30, 2010  Sirio 
20110181292  July 28, 2011  Oowada 
20120014138  January 19, 2012  Ngo 
20140312789  October 23, 2014  Feng 
20140313790  October 23, 2014  Feng 
20150194909  July 9, 2015  Pahlevaninezhad 
 F. Krismer et al: “Acutate SamllSignal Model for the Digital Control of an Automotive Bidirectional Dual Active Bringe”, IEE Transaction on Power Electronics, vol. 24 No. 12, Dec. 1, 2009.
 Partial Search Report from Patent Cooperation Treat No. PCT/US2015/033852 filed Jun. 2, 2015, mailed Sep. 23, 2015.
 F. Kismer et al, Accurate SmallSignal Model for the Digital Control of an Automotive Didirectional Dual Active Bridge, IEE Transactions on Power Electronics, vol. 24, No. 12, Dec. 1, 2009 (Dec. 1, 2009), pp. 27562768, XP055213479, ISSN 08858993, D01: 10.1109/TPEL.20092027904 p. 2763; figures 1,2,6.
 International Searching Authority, Notification of Transmittal of The International Search Report a, 14 Dnd The Written Opinion of the International Searching Authority, or the Declaration of PCT Application No. PCT/US2015/033852, International Filing Date of Jun. 2, 2015, Mailed Dec. 14, 2015.
 U.S. Appl. No. 14/728,837, filed Jun. 2, 2015, Notice of Allowance mailed Oct. 13, 2016.
 U.S. Appl. No. 14/728,890, filed Jun. 2, 2015, Notice of Allowance mailed Oct. 27, 2016.
Type: Grant
Filed: Jun 2, 2015
Date of Patent: Jul 18, 2017
Patent Publication Number: 20150349648
Assignee: UTAH STATE UNIVERSITY (North Logan, UT)
Inventors: Regan A Zane (North Logan, UT), Daniel Seltzer (Los Angeles, CA), Dragan Maksimovic (Boulder, CO), Boris Jacobson (Westford, MA), Donald Desrosiers (Marlborough, MA)
Primary Examiner: Jeffrey Gblende
Assistant Examiner: Ishrat Jamali
Application Number: 14/728,866
International Classification: H02M 3/335 (20060101); H02M 7/538 (20070101); H02M 1/42 (20070101); H02M 3/158 (20060101); H02M 7/5387 (20070101); H02M 7/48 (20070101); H02M 1/00 (20060101);